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Artykuły w czasopismach na temat „Instability exponential equation”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

SCHEUTZOW, MICHAEL. "EXPONENTIAL GROWTH RATES FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 05, no. 02 (2005): 163–74. http://dx.doi.org/10.1142/s0219493705001468.

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In this survey, we provide some tools to obtain estimates for the almost sure exponential growth rate of a stochastic delay differential equation (sdde) which fixes zero. In particular, we are interested in determining whether the solutions of a given sdde are exponentially stable (i.e. have a negative exponential growth rate) or not. We focus on equations without drift, which are a good testground to assess if a method is powerful enough to discriminate between stability and instability when a certain parameter (e.g. noise intensity) varies. The most powerful tool we provide is the method of

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2

Kalashnik, M. V. "Shear Flow Instability over a Finite Time Interval." Известия Российской академии наук. Физика атмосферы и океана 59, no. 2 (2023): 165–72. http://dx.doi.org/10.31857/s0002351523020037.

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Within the framework of a discrete quasi-geostrophic model with two vertical levels, the problem of linear stability of the flow of a stratified rotating fluid with constant vertical and horizontal velocity shifts is solved. It is shown that taking into account the horizontal shear leads to a qualitative change in the dynamics of unstable wave disturbances. The main feature is related to the effect of temporary exponential growth of unstable perturbations, i.e. growth over a finite time period. This effect manifests itself in the alternation of stages of smooth oscillating behavior (in time) w

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3

Mandache, Niculae. "Exponential instability in an inverse problem for the Schrödinger equation." Inverse Problems 17, no. 5 (2001): 1435–44. http://dx.doi.org/10.1088/0266-5611/17/5/313.

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4

Kuznetsov, V. D. "Magnetic Buoyancy with Viscosity and Ohmic Dissipation and Flux Tube Formation." Symposium - International Astronomical Union 142 (1990): 58–59. http://dx.doi.org/10.1017/s0074180900087726.

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In the framework of the magnetohydrodynamic equations with dissipative terms in the form of turbulent viscosity (Vt) the linear stage of the instability of a subphotospheric field with respect to magnetic buoyancy is considered. For an exponential in z, isothermal plane-parallel atmosphere with a constant Alfvenic velocity the perturbations of the form are described by differential equation with constant coefficients. The qualitative dependence of the growth rate of instability on transverse wave number is determined (see Figures 1 and 2) and characteristic scales of the magnetic tubes are eva

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5

Kosheleva, Elena. "On the Dynamic Stability of a Reinforced Concrete Plate, Taking into Account the Material Creep." MATEC Web of Conferences 196 (2018): 01025. http://dx.doi.org/10.1051/matecconf/201819601025.

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The problem of the dynamic stability of a reinforced concrete plate armoured in two directions parallel to its edges is considered. To describe the viscoelastic properties of concrete, an integral dependence was adopted with an exponential kernel. The use of this dependence led to a linear differential equation of plate vibration. In addition to the creep of concrete, the work of the reinforcement was taken into account. The solution of the differential equation of vibrations of a plate in the form of a series with separated variables is considered, which satisfies the plate fastening conditio

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6

Afful, Adusei-Poku, and Ernest Yankson. "Exponential stability and instability in nonlinear differential equations with multiple delays." Proyecciones (Antofagasta) 42, no. 3 (2023): 681–93. http://dx.doi.org/10.22199/issn.0717-6279-4197.

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Inequalities regarding the solutions of the nonlinear differential equation with multiple delays xl(t) = a(t)f(x(t)) +Σni=1bi(t)f(x(t − hi)), are obtained by means of Lyapunov functionals. These inequalities are then used to obtain sufficient conditions that guarantee exponential decay of solutions to zero of the multi delay nonlinear differential equation. In addition, we obtain a criterion for the instability of the zero solution. The results generalizes some results in the literature.

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7

Kelleche, Abdelkarim, and Amirouche Berkani. "On exponential stabilization of a nonlinear neutral wave equation." Boletim da Sociedade Paranaense de Matemática 41 (December 23, 2022): 1–10. http://dx.doi.org/10.5269/bspm.52132.

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This work aims to study a nonlinear wave equation subject to a delay of neutral type. The nonlinearity and the delay appear in the second time derivative. In spite of the fact that delays by nature, have an instability effect on the structures, the strong damping is sufficient to allow the system to reach its equilibrium state with an exponential manner. The difficulties arising from the nonlinearity have been overcome by using an inequality due to a Sobolev embedding theorem. The main result has been established without any condition on the coefficient of the neutral delay.

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8

Grimshaw, Roger. "Two-dimensional modulation instability of wind waves." Journal of Ocean Engineering and Marine Energy 5, no. 4 (2019): 413–17. http://dx.doi.org/10.1007/s40722-019-00146-7.

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Abstract It is widely known that deep-water waves are modulationally unstable and that this can be modelled by a nonlinear Schrödinger equation. In this paper, we extend the previous studies of the effect of wind forcing on this instability to water waves in finite depth and in two horizontal space dimensions. The principal finding is that the instability is enhanced and becomes super-exponential and that the domain of instability in the modulation wavenumber space is enlarged. Since the outcome of modulation instability is expected to be the generation of rogue waves, represented within the f

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9

SAANOUNI, T. "GLOBAL WELL-POSEDNESS AND INSTABILITY OF A NONLINEAR SCHRÖDINGER EQUATION WITH HARMONIC POTENTIAL." Journal of the Australian Mathematical Society 98, no. 1 (2014): 78–103. http://dx.doi.org/10.1017/s1446788714000391.

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AbstractThis paper is concerned with the Cauchy problem for a nonlinear Schrödinger equation with a harmonic potential and exponential growth nonlinearity in two space dimensions. In the defocusing case, global well-posedness is obtained. In the focusing case, existence of nonglobal solutions is discussed via potential-well arguments.

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10

Deka, Pranab J., and Lukas Einkemmer. "Exponential Integrators for Resistive Magnetohydrodynamics: Matrix-free Leja Interpolation and Efficient Adaptive Time Stepping." Astrophysical Journal Supplement Series 259, no. 2 (2022): 57. http://dx.doi.org/10.3847/1538-4365/ac5177.

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Abstract We propose a novel algorithm for the temporal integration of the resistive magnetohydrodynamics (MHD) equations. The approach is based on exponential Rosenbrock schemes in combination with Leja interpolation. It naturally preserves Gauss’s law for magnetism and is unencumbered by the stability constraints observed for explicit methods. Remarkable progress has been achieved in designing exponential integrators and computing the required matrix functions efficiently. However, employing them in MHD simulations of realistic physical scenarios requires a matrix-free implementation. We show

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11

Badawi, Haidar, Mohammad Akil, and Zayd Hajjej. "Stability and instability of Kirchhoff plate equations with delay on the boundary control." Electronic Journal of Differential Equations 2023, no. 01-?? (2023): 68. http://dx.doi.org/10.58997/ejde.2023.68.

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In this article, we consider the Kirchhoff plate equation with delay terms on the boundary control. We give instability examples of systems for some choices of delays. Finally, we prove its well-posedness, strong stability, and exponential stability under a multiplier geometric control condition. Foro more information see https://ejde.math.txstate.edu/Volumes/2023/68/abstr.html

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12

Steer, James N., Mark L. McAllister, Alistair G. L. Borthwick, and Ton S. van den Bremer. "Experimental Observation of Modulational Instability in Crossing Surface Gravity Wavetrains." Fluids 4, no. 2 (2019): 105. http://dx.doi.org/10.3390/fluids4020105.

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The coupled nonlinear Schrödinger equation (CNLSE) is a wave envelope evolution equation applicable to two crossing, narrow-banded wave systems. Modulational instability (MI), a feature of the nonlinear Schrödinger wave equation, is characterized (to first order) by an exponential growth of sideband components and the formation of distinct wave pulses, often containing extreme waves. Linear stability analysis of the CNLSE shows the effect of crossing angle, θ , on MI, and reveals instabilities between 0 ∘ < θ < 35 ∘ , 46 ∘ < θ < 143 ∘ , and 145 ∘ < θ < 180 ∘ . Herein, the mod

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13

KALTENBACHER, BARBARA, IRENA LASIECKA, and MARIA K. POSPIESZALSKA. "WELL-POSEDNESS AND EXPONENTIAL DECAY OF THE ENERGY IN THE NONLINEAR JORDAN–MOORE–GIBSON–THOMPSON EQUATION ARISING IN HIGH INTENSITY ULTRASOUND." Mathematical Models and Methods in Applied Sciences 22, no. 11 (2012): 1250035. http://dx.doi.org/10.1142/s0218202512500352.

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We consider a third order in time equation which arises, e.g. as a model for wave propagation in viscous thermally relaxing fluids. This equation displays, even in the linear version, a variety of dynamical behaviors for its solution that depend on the physical parameters in the equation. These range from non-existence and instability to exponential stability (in time) as was shown for the constant coefficient case in Ref. 23. In case of vanishing diffusivity of the sound, there is a lack of generation of a semigroup associated with the linear dynamics. If diffusivity of the sound is positive,

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14

Quintanilla, Ramón. "Moore–Gibson–Thompson thermoelasticity." Mathematics and Mechanics of Solids 24, no. 12 (2019): 4020–31. http://dx.doi.org/10.1177/1081286519862007.

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We consider a thermoelastic theory where the heat conduction is described by the Moore–Gibson–Thompson equation. In fact, this equation can be obtained after the introduction of a relaxation parameter in the Green–Naghdi type III model. We analyse the one- and three-dimensional cases. In three dimensions, we obtain the well-posedness and the stability of solutions. In one dimension, we obtain the exponential decay and the instability of the solutions depending on the conditions over the system of constitutive parameters. We also propose possible extensions for these theories.

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15

MILES, JOHN. "A note on surface waves generated by shear-flow instability." Journal of Fluid Mechanics 447 (October 30, 2001): 173–77. http://dx.doi.org/10.1017/s0022112001005833.

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Morland, Saffman & Yuen's (1991) study of the stability of a semi-infinite, concave shear flow bounded above by a capillary–gravity wave, for which they obtained numerical solutions of Rayleigh's equation, is revisited. A variational formulation is used to construct an analytical description of the unstable modes for the exponential velocity profile U = U0 exp(y/d), −∞ < y [les ] 0. The assumption of slow waves ([mid ]c[mid ] [Lt ] U0) yields an approximation that agrees with the numerical results of Morland et al. The assumption of short waves (kd [Gt ] 1) yields Shrira's (1993) asympt

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16

Yoon, Peter H., Rodrigo A. López, Jungjoon Seough, et al. "Quasi-linear Analysis of Proton-cyclotron Instability." Astrophysical Journal 976, no. 2 (2024): 173. http://dx.doi.org/10.3847/1538-4357/ad86be.

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Abstract The proton-cyclotron (PC) instability operates in various space plasma environments. In the literature, the so-called velocity moment-based quasi-linear theory is employed to investigate the physical process of PC instability that takes place after the onset of early linear exponential growth. In this method, the proton velocity distribution function (VDF) is assumed to maintain a bi-Maxwellian form for all time, which substantially simplifies the analysis, but its validity has not been rigorously examined by comparing against the actual solution of the kinetic equation. The present p

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17

Bin Jebreen, Haifa, and Yurilev Chalco-Cano. "Application of the Multiple Exp-Function, Cross-Kink, Periodic-Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation." Advances in Mathematical Physics 2021 (January 15, 2021): 1–12. http://dx.doi.org/10.1155/2021/6643512.

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In this article, the exact wave structures are discussed to the Caudrey-Dodd-Gibbon equation with the assistance of Maple based on the Hirota bilinear form. It is investigated that the equation exhibits the trigonometric, hyperbolic, and exponential function solutions. We first construct a combination of the general exponential function, periodic function, and hyperbolic function in order to derive the general periodic-kink solution for this equation. Then, the more periodic wave solutions are presented with more arbitrary autocephalous parameters, in which the periodic-kink solution localized

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18

Thorpe, S. A., and Zhiyu Liu. "Marginal Instability?" Journal of Physical Oceanography 39, no. 9 (2009): 2373–81. http://dx.doi.org/10.1175/2009jpo4153.1.

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Abstract Some naturally occurring, continually forced, turbulent, stably stratified, mean shear flows are in a state close to that in which their stability changes, usually from being dynamically unstable to being stable: the time-averaged flows that are observed are in a state of marginal instability. By “marginal instability” the authors mean that a small fractional increase in the gradient Richardson number Ri of the mean flow produced by reducing the velocity and, hence, shear is sufficient to stabilize the flow: the increase makes Rimin, the minimum Ri in the flow, equal to Ric, the criti

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19

Kalashnik, M. V., M. V. Kurgansky, and S. V. Kostrykin. "Instability of Surface Quasigeostrophic Spatially Periodic Flows." Journal of the Atmospheric Sciences 77, no. 1 (2019): 239–55. http://dx.doi.org/10.1175/jas-d-19-0100.1.

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Abstract The surface quasigeostrophic (SQG) model is developed to describe the dynamics of flows with zero potential vorticity in the presence of one or two horizontal boundaries (Earth surface and tropopause). Within the framework of this model, the problems of linear and nonlinear stability of zonal spatially periodic flows are considered. To study the linear stability of flows with one boundary, two approaches are used. In the first approach, the solution is sought by decomposing into a trigonometric series, and the growth rate of the perturbations is found from the characteristic equation

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20

Akagi, Goro, and Ryuji Kajikiya. "Stability of stationary solutions for semilinear heat equations with concave nonlinearity." Communications in Contemporary Mathematics 17, no. 06 (2015): 1550001. http://dx.doi.org/10.1142/s0219199715500017.

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This paper is concerned with the stability analysis of stationary solutions of the Cauchy–Dirichlet problem for some semilinear heat equation with concave nonlinearity. The instability of sign-changing solutions is verified under some variational assumption. Moreover, the exponential stability of the positive stationary solution at an optimal rate is proved by exploiting a super–subsolution method as well as the parabolic regularity theory. The base of our analysis relies on the linearization of the equation at each stationary solution and spectral analysis of the corresponding linearized oper

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21

TSAI, CHIA-CHENG, and PO-HO LIN. "ON THE EXPONENTIAL CONVERGENCE OF THE METHOD OF FUNDAMENTAL SOLUTIONS." International Journal of Computational Methods 10, no. 02 (2013): 1341007. http://dx.doi.org/10.1142/s0219876213410077.

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It is well known that the method of fundamental solutions (MFS) is a numerical method of exponential convergence. In other words, the logarithmic error is proportional to the node number of spatial discretization. In this study, the exponential convergence of the MFS is demonstrated by solving the Laplace equation in domains of rectangles, ellipses, amoeba-like shapes, and rectangular cuboids. In the solution procedure, the sources of the MFS are located as far as possible and the instability resulted from the ill-conditioning of system matrix is avoided by using the multiple precision floatin

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22

Gupta, N. K., and S. V. Lawande. "Rayleigh–Taylor instability in multi-structured inertial confinement fusion targets." Laser and Particle Beams 7, no. 1 (1989): 27–54. http://dx.doi.org/10.1017/s0263034600005826.

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A formalism for the analysis of the Rayleigh–Taylor instability in the multi-structured solid or shell targets is presented. The formulation covers both the plane and the curved geometry targets. A generalized eigenvalue equation for the exponential growth rate of the instability is derived along with the necessary boundary conditions. Analytical solutions for the growth rate are presented for some elementary density profiles and a comparative study is made between the plane, cylindrical and spherical targets. The solution for the step function density profile is generalized for any number Nof

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23

Maslowe, Sherwin A. "Linear instability of a perturbed Lamb–Oseen vortex." Fluid Dynamics Research 54, no. 1 (2022): 015513. http://dx.doi.org/10.1088/1873-7005/ac522d.

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Abstract This paper presents an investigation of the stability of a vortex with azimuthal velocity profile V ˉ = 1 − 1 − ε r 2 e − r 2 / r . When ε = 0, the Lamb–Oseen vortex model is recovered. Although the Lamb–Oseen vortex supports propagating waves known as Kelvin waves, the flow is stable according to Rayleigh’s circulation criterion. In this paper, on the other hand, the modified vortex profile admits linearly unstable disturbances for ε > 0 and we investigate their characteristics. These may be either axisymmetric or non-axisymmetric, but we find that the axisymmetric perturbations h

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24

MAJDA, ANDREW J., and MICHAEL G. SHEFTER. "Elementary stratified flows with instability at large Richardson number." Journal of Fluid Mechanics 376 (December 10, 1998): 319–50. http://dx.doi.org/10.1017/s0022112098003085.

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In contrast to the Miles–Howard theorem for inviscid steady shear flow in stably stratified fluids, explicit elementary time-periodic solutions of the Boussinesq equations are developed here which are unstable for arbitrarily large Richardson numbers. These elementary flows are parameterized through solutions of a nonlinear pendulum equation and involve spatially constant but temporally varying vorticity and density gradients which interact through advection and baroclinic vorticity production. Exact nonlinear solutions for arbitrary wave-like disturbances for these flows are developed here an

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25

Myung, Yun Soo, Taeyoon Moon, and Young-Jai Park. "Einstein-singleton theory and its power spectra in de Sitter inflation." International Journal of Modern Physics D 25, no. 14 (2016): 1650107. http://dx.doi.org/10.1142/s0218271816501078.

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We study the Einstein-singleton theory during de Sitter inflation since it provides a way to degenerate fourth-order scalar theory. We obtain an exact solution expressed in terms of the exponential-integral function by solving the degenerate fourth-order scalar equation in de Sitter spacetime. Furthermore, we find that its power spectrum blows negatively up in the superhorizon limit, while it is negatively scale-invariant in the subhorizon limit. This suggests that the Einstein-singleton theory contains the ghost-instability and thus, it is not suitable for developing a slow-roll inflation mod

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26

Orefi, Abu, and Adakole Omojo. "Growth and Instability in Selected Cereal Crops in Benue State, Nigeria and Its Implications for Food Security." Asian Research Journal of Agriculture 5, no. 2 (2017): 1–8. https://doi.org/10.9734/ARJA/2017/33100.

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This study was carried out to determine growth rate and instability in area, output and yield of selected cereals and its implications for food security in Benue State, Nigeria from 1986 to 2012. In addition, sources of growth in output were also examined. To achieve this, exponential trend equation, Cuddy-Della Valle index (CDVI) and decomposition analysis were employed. The estimated compound growth rates for area of maize, millet, rice and sorghum were 4.3%, 9.8%, 1.8% and -2.4% respectively. Compound growth rates of output were 4.7%, 13.1%, 12.6% and 0.9% for maize, millet, rice and sorghu

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27

Yi, Yun-Bo. "Finite Element Analysis of Thermoelastodynamic Instability Involving Frictional Heating." Journal of Tribology 128, no. 4 (2006): 718–24. http://dx.doi.org/10.1115/1.2345412.

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A finite element method is used to solve the problem involving thermoelastodynamic instability (TEDI) in frictional sliding systems. The resulting matrix equation contains a complex eigenvalue that represents the exponential growth rate of temperature, displacement, and velocity fields. Compared to the thermoelastic instability (TEI) in which eigenmodes always decay with time when the sliding speed is below a critical value, numerical results from TEDI have shown that some of the modes always grow in the time domain at any sliding speed. As a result, when the inertial effect is considered, the

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28

Xue, Zongan, Yanyan Ma, Shengjian Wang, Huayu Hu, and Qingqing Li. "A Multi-Task Learning Framework of Stable Q-Compensated Reverse Time Migration Based on Fractional Viscoacoustic Wave Equation." Fractal and Fractional 7, no. 12 (2023): 874. http://dx.doi.org/10.3390/fractalfract7120874.

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Q-compensated reverse time migration (Q-RTM) is a crucial technique in seismic imaging. However, stability is a prominent concern due to the exponential increase in high-frequency ambient noise during seismic wavefield propagation. The two primary strategies for mitigating instability in Q-RTM are regularization and low-pass filtering. Q-RTM instability can be addressed through regularization. However, determining the appropriate regularization parameters is often an experimental process, leading to challenges in accurately recovering the wavefield. Another approach to control instability is l

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29

Arshad, Muhammad, Aly R. Seadawy, Dianchen Lu, and Farhan Ali. "Solitary wave solutions of Kaup–Newell optical fiber model in mathematical physics and its modulation instability." Modern Physics Letters B 34, no. 26 (2020): 2050277. http://dx.doi.org/10.1142/s0217984920502772.

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Soliton solutions which signify long wave parallel to the magnetic fields of Kaup–Newell optical fiber model are discussed in this paper by two different methods. The improved simple equation method (ISEM) and exp[Formula: see text]-expansion scheme are employed to solve the model to construct the solutions of the model in different cases. The achieved solutions are represented in different and general forms such as logarithmic or exponential function, trigonometric and hyperbolic trigonometric functions, etc. Also, the modulation instability of the model is analyzed which confirms that all ob

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30

Pálmai, Zoltán. "Chaotic Phenomena in Fast Plastic Deformation (in the Case of Cutting)." Materials Science Forum 473-474 (January 2005): 369–74. http://dx.doi.org/10.4028/www.scientific.net/msf.473-474.369.

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Technologies applied in machining metals are often characterised by highly localised shear strain, which can be regarded nearly as adiabatic, and which might lead to thermoplastic instability in certain cases. In cutting, similar incidents can be observed in the shear zone, in which γ=2–50, dγ/dt≈104 s-1, dT/dt=106 K/s, and under such extreme conditions chaotic phenomena may occur occasionally. Chip formation can be described by a two-dimensional model, where the variation of shear stress τ and temperature T in time are given by autonomous differential equations, while the material characteris

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31

Protas, Bartosz, and Takashi Sakajo. "Harnessing the Kelvin–Helmholtz instability: feedback stabilization of an inviscid vortex sheet." Journal of Fluid Mechanics 852 (August 3, 2018): 146–77. http://dx.doi.org/10.1017/jfm.2018.523.

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In this investigation, we use a simple model of the dynamics of an inviscid vortex sheet given by the Birkhoff–Rott equation to obtain fundamental insights about the potential for stabilization of shear layers using feedback control. As actuation, we consider two arrays of point sinks/sources located a certain distance above and below the vortex sheet and subject to the constraint that their mass fluxes separately add up to zero. First, we demonstrate using analytical computations that the Birkhoff–Rott equation linearized around the flat-sheet configuration is in fact controllable when the nu

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32

Mazilu, Traian. "Numerically Stable form of Green’s Function for a Free-Free Uniform Timoshenko Beam." Mathematics 11, no. 1 (2022): 86. http://dx.doi.org/10.3390/math11010086.

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Beam models are widely applied in civil engineering, transport, and industry because the beams are basic structural elements. When dealing with the high-order modes of beam in the context of applying the modal analysis method, the numerical instability issue affects the numeric simulation accuracy in many boundary conditions. There are two solutions in literature to overcome this shortcoming, namely refinement of the asymptotic form for the high order modes and reshaping the terms within the equation of the modes to eliminate the source of the numerical instability. In this paper, the numerica

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33

Nizamova, A. D., V. N. Kireev, and S. F. Urmancheev. "Research of eigenfuctions perturbation of the transverse component velocity thermoviscous liquids flow." Multiphase Systems 14, no. 2 (2019): 132–37. http://dx.doi.org/10.21662/mfs2019.2.018.

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The viscous model fluid flow in a plane channel with a linear temperature profile is considered. The problem of the thermoviscous fluid flow stability is solved on the basis of the previously obtained generalized Orr–Sommerfeld equation by the spectral method of decomposition into Chebyshev polynomials. We study the effect of taking into account the linear and exponential dependences of the viscosity of a liquid on temperature on the eigenfunctions of the hydrodynamic stability equation and on perturbations of the transverse velocity of an incompressible fluid in a plane channel when various w

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34

Hultgren, Lennart S. "Nonlinear spatial equilibration of an externally excited instability wave in a free shear layer." Journal of Fluid Mechanics 236 (March 1992): 635–64. http://dx.doi.org/10.1017/s0022112092001563.

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A two-dimensional disturbance evolving from a strictly linear, finite-growth-rate instability wave with nonlinear effects first becoming important in the critical layer is considered. The analysis is carried out for a general weakly non-parallel mean flow using matched asymptotic expansions. The flow in the critical layer is governed by a nonlinear vorticity equation which includes a spatial-evolution term. As in Goldstein & Hultgren (1988), the critical layer ages into a quasi-equilibrium one and the initial exponential growth of the instability wave is converted into a weak algebraic gro

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35

Abdalla, Mohamed, Md Mamunur Roshid, Mahtab Uddin, and Mohammad Safi Ullah. "Analysis Modulation Instability and Parametric Effect on Soliton Solutions for M-Fractional Landau–Ginzburg–Higgs (LGH) Equation Through Two Analytic Methods." Fractal and Fractional 9, no. 3 (2025): 154. https://doi.org/10.3390/fractalfract9030154.

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This manuscript studies the M-fractional Landau–Ginzburg–Higgs (M-fLGH) equation in comprehending superconductivity and drift cyclotron waves in radially inhomogeneous plasmas, especially for coherent ion cyclotron wave propagation, aiming to explore the soliton solutions, the parameter’s effect, and modulation instability. Here, we propose a novel approach, namely a newly improved Kudryashov’s method that integrates the combination of the unified method with the generalized Kudryashov’s method. By employing the modified F-expansion and the newly improved Kudryashov’s method, we investigate th

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Peral, I., and J. L. Vazquez. "On the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term." Archive for Rational Mechanics and Analysis 129, no. 3 (1995): 201–24. http://dx.doi.org/10.1007/bf00383673.

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Alharthi, Nadiyah Hussain, Melike Kaplan, and Rubayyi T. Alqahtani. "Soliton Dynamics and Modulation Instability in the (3+1)-Dimensional Generalized Fractional Kadomtsev–Petviashvili Equation." Symmetry 17, no. 5 (2025): 666. https://doi.org/10.3390/sym17050666.

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In this article, novel methods of analysis to solve the (3+1)-dimensional generalized fractional Kadomtsev–Petviashvili equation, which plays a crucial role in the modelling of fluid dynamics, particularly wave propagation in complicated media, are presented. The fractional KP equation, a well-established mathematical model, uses fractional derivatives to more adequately describe more general types of nonlinear wave phenomena, with a richer and improved understanding of the dynamics of fluids with non-classical characteristics, such as anomalous diffusion or long-range interactions. Two effici

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Yuen, David A., Marc R. Saari, and Gerald Schubert. "Explosive Growth of Shear-Heating Instabilities in the Down-Slope Creep of Ice Sheets." Journal of Glaciology 32, no. 112 (1986): 314–20. http://dx.doi.org/10.1017/s0022143000011977.

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AbstractThe time-scale for the onset of the explosive growth of a finite-amplitude shear-heating instability in the down-slope creep of a thick ice sheet is determined by integrating the equation for the temporal evolution of the temperature-depth profile subsequent to a sudden change in ice thickness. All instabilities eventually grow explosively after a prolonged period of simmering or relatively slow monotonic growth. Though times for explosive growth depend on initial and final ice thicknesses, surface temperature, accumulation rate, basal heat flux, and ice rheological parameters, the exp

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Yuen, David A., Marc R. Saari, and Gerald Schubert. "Explosive Growth of Shear-Heating Instabilities in the Down-Slope Creep of Ice Sheets." Journal of Glaciology 32, no. 112 (1986): 314–20. http://dx.doi.org/10.3189/s0022143000011977.

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AbstractThe time-scale for the onset of the explosive growth of a finite-amplitude shear-heating instability in the down-slope creep of a thick ice sheet is determined by integrating the equation for the temporal evolution of the temperature-depth profile subsequent to a sudden change in ice thickness. All instabilities eventually grow explosively after a prolonged period of simmering or relatively slow monotonic growth. Though times for explosive growth depend on initial and final ice thicknesses, surface temperature, accumulation rate, basal heat flux, and ice rheological parameters, the exp

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León-Ramírez, Alejandro, Oswaldo González-Gaxiola, and Guillermo Chacón-Acosta. "Analytical Solutions to the Chavy-Waddy–Kolokolnikov Model of Bacterial Aggregates in Phototaxis by Three Integration Schemes." Mathematics 11, no. 10 (2023): 2352. http://dx.doi.org/10.3390/math11102352.

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In this work, we find analytical solutions to the Chavy-Waddy–Kolokolnikov equation, a continuum approximation for modeling aggregate formation in bacteria moving toward the light, also known as phototaxis. We used three methods to obtain the solutions, the generalized Kudryashov method, the e−R(ξ)-expansion, and exponential function methods, all of them being very efficient for finding traveling wave-like solutions. Findings can be classified into the case where the nonlinear term can be considered a small perturbation of the linear case and the regime of instability and pattern formation. St

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MIGLIORATI, M., A. SCHIAVI, and G. DATTOLI. "SIMULATIONS OF COHERENT SYNCHROTRON RADIATION EFFECTS IN ELECTRON MACHINES." International Journal of Modern Physics A 22, no. 23 (2007): 4235–44. http://dx.doi.org/10.1142/s0217751x07037780.

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Coherent synchrotron radiation (CSR) generated by high intensity electron beams can be a source of undesirable effects limiting the performance of storage rings. The complexity of the physical mechanisms underlying the interplay between the electron beam and the CSR demands for reliable simulation codes. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problems in accelerators. The extension of these methods to the non linear case is ideally suited to treat wakefields - beam interaction. In this paper we report on the development of a numerical c

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Dosser, Hayley V., and Bruce R. Sutherland. "Anelastic Internal Wave Packet Evolution and Stability." Journal of the Atmospheric Sciences 68, no. 12 (2011): 2844–59. http://dx.doi.org/10.1175/jas-d-11-097.1.

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Abstract As upward-propagating anelastic internal gravity wave packets grow in amplitude, nonlinear effects develop as a result of interactions with the horizontal mean flow that they induce. This qualitatively alters the structure of the wave packet. The weakly nonlinear dynamics are well captured by the nonlinear Schrödinger equation, which is derived here for anelastic waves. In particular, this predicts that strongly nonhydrostatic waves are modulationally unstable and so the wave packet narrows and grows more rapidly in amplitude than the exponential anelastic growth rate. More hydrostati

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Xie, Yuan-Xi. "Explicit and accurate solutions for the Benney equation." Journal of AppliedMath 3, no. 2 (2025): 2899. https://doi.org/10.59400/jam2899.

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The Benney equation arises from many different physical contexts as an appropriately real physical model equation involving a lot of effects of dispersion, dissipation, nonlinearity, and instability. As a result, it is a very important and challenging theme to search for the explicit and accurate traveling wave solutions of the Benney equation. In this paper, by introducing an ansatz solution with two E-exponential functions, we have made some improvements to the trial function approach for solving three NPDEs proposed by Xie and Tang. On this basis, we have put forward a direct trial function

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S More, Sachin, K. V. Deshmukh, and R. V. Chavan. "Has Production of Cotton in Maharashtra Shown Stable Growth Over the Years ?" Current Agriculture Research Journal 8, no. 3 (2020): 224–31. http://dx.doi.org/10.12944/carj.8.3.08.

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The growth and instability in area, production and yield of cotton in Maharashtra was assessed before and after introduction of Bt cotton varieties. The study aims to know the growth behavior of cotton production over the years. The contribution of area and productivity towards cotton production was measured by decomposing the cotton production series. The method proposed by Minhas and Vidhyanathan and reframed by Sharma was employed. The compound growth rate was estimated on the basis of fit using non-linear model i.e. exponential. The fitted equation was estimated using marquardt algorithms.

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Tahiru, Solomon, and Oluwole Daniel Makinde. "Analysis of Nonlinear Heat Transfer in a Cylindrical Solid with Two-Step Exothermic Kinetics and Radiative Heat Loss." Defect and Diffusion Forum 377 (September 2017): 17–28. http://dx.doi.org/10.4028/www.scientific.net/ddf.377.17.

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This paper examines the problem of nonlinear heat transfer in a cylindrical solid of combustible materials with two-step exothermic kinetics and radiative heat loss to the ambient surrounding. The reactant diffusion and temperature dependent pre-exponential factors with respect to sensitized, Arrhenius, and bimolecular kinetics are taken into account in the model energy balanced equation. Both regular perturbation method and numerical shooting technique coupled with Runge-Kutta-Fehlberg iteration scheme are employed to tackle the nonlinear model problem. The effects of various thermophysical p

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Tang, Zhiren, Chaofeng Liu, Hongbo Jiang, Feiyu Hou, and Shenglan Wang. "Analyzing the Effect of Tethered Cable on the Stability of Tethered UAVs Based on Lyapunov Exponents." Applied Sciences 14, no. 10 (2024): 4253. http://dx.doi.org/10.3390/app14104253.

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In the working process of the tethered unmanned aerial vehicle (UAV), there is interference from the tethered cable, which can easily lead to the instability of the UAV. To solve the above problems, a method based on the Lyapunov exponent is proposed to analyze the stability of tethered cables for tethered UAVs. The dynamics equation of the UAV platform is established using the Euler–Poincare equation. The tension formula of the tethered cable is derived from the catenary theory and the principle of micro-segment equilibrium. Based on the Lyapunov exponential method, the stability changes of t

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Villani, Vincenzo. "Viscosity Flow Curves of Agar and the Bounded Ripening Growth Model of the Gelation Onset." Molecules 29, no. 6 (2024): 1293. http://dx.doi.org/10.3390/molecules29061293.

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The gelation kinetics of agar aqueous solutions were studied by means of the viscosity flow curves using a coaxial Couette cylinder viscometer. The viscosity curves show an unusual sigmoidal trend or an exponential decay to a viscous steady state. An original theory of gelation kinetics was developed considering the coarsening of increasingly larger and more stable clusters due to Ostwald ripening and the breakup of clusters that were too large due to the instability of rotating large particles induced by the shear rate. The developed Bounded Ripening Growth model takes into account the trend

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Khalifa, Abeer S., Hamdy M. Ahmed, Niveen M. Badra, Wafaa B. Rabie, Farah M. Al-Askar, and Wael W. Mohammed. "New soliton wave structure and modulation instability analysis for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities." AIMS Mathematics 9, no. 9 (2024): 26166–81. http://dx.doi.org/10.3934/math.20241278.

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<p>We have introduced various novel soliton waves and other analytic wave solutions for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities. The modified extended direct algebraic method governs the transmission of various solitons with different effects. The combination of this system enables the obtaining of analytical soliton solutions with some unique behaviors, including bright, dark, and mixed dark-bright soliton solutions; singular soliton solutions; singular periodic, exponential, rational wave solutions; and Jacobi elliptic function solutions. Th

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LUTEPHY, Mohsen, Botir Berdiyorovich ISMAILOV, and Adnan Hashim ABDULKADHIM. "Clockwise and counter clockwise 6 & 9 year geostrophic MC (& Rossby) waves in centre of the mechanism of geomagnetic jerks and relevant LODs." Contributions to Geophysics and Geodesy 52, no. 1 (2022): 127–55. http://dx.doi.org/10.31577/congeo.2022.52.1.6.

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Versus the theory of fully stochastically mechanism of geomagnetic jerks based on the buoyant force driven Quasi-Geostrophic (QG) dynamo, the torsional waves in realistic condition of the Earth's core evolve in the intradecadal time scales. Geostrophic slow MC (& Rossby) waves as entanglement of inertial and Alfvén waves are the source of 6 & 9 year geomagnetic secular variations inferred with intradecadal variations in the Earth's rotation rate defined by length of day. From MHD equations in the Earth's liquid metal core, we find a suit of equations equivalent with Hall-MHD in plasma

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LUTEPHY, Mohsen, Botir Berdiyorovich ISMAILOV, and Adnan Hashim ABDULKADHIM. "Clockwise and counter clockwise 6 & 9 year geostrophic MC (& Rossby) waves in centre of the mechanism of geomagnetic jerks and relevant LODs." Contributions to Geophysics and Geodesy 52, no. 1 (2022): 127–55. http://dx.doi.org/10.31577/congeo.2022.52.1.6.

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Versus the theory of fully stochastically mechanism of geomagnetic jerks based on the buoyant force driven Quasi-Geostrophic (QG) dynamo, the torsional waves in realistic condition of the Earth's core evolve in the intradecadal time scales. Geostrophic slow MC (& Rossby) waves as entanglement of inertial and Alfvén waves are the source of 6 & 9 year geomagnetic secular variations inferred with intradecadal variations in the Earth's rotation rate defined by length of day. From MHD equations in the Earth's liquid metal core, we find a suit of equations equivalent with Hall-MHD in plasma

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