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Journal articles on the topic 'Weakly nonlinear analysi'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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1

Zheng, Kelong, Wenqiang Feng, and Chunxiang Guo. "Some New Nonlinear Weakly Singular Inequalities and Applications to Volterra-Type Difference Equation." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/912874.

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Some new nonlinear weakly singular difference inequalities are discussed, which generalize some known weakly singular inequalities and can be used in the analysis of nonlinear Volterra-type difference equations with weakly singular kernel. An application to the upper bound of solutions of a nonlinear difference equation is also presented.

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2

Cheng, Kelong, Chunxiang Guo, and Qingke Zeng. "On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/795456.

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Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels. A few applications to the upper bound and the uniqueness of solutions of nonlinear difference equations are also involved.

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3

HUNTER, JOHN K. "SHORT-TIME EXISTENCE FOR SCALE-INVARIANT HAMILTONIAN WAVES." Journal of Hyperbolic Differential Equations 03, no. 02 (2006): 247–67. http://dx.doi.org/10.1142/s0219891606000781.

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We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations include ones that describe weakly nonlinear hyperbolic surface waves, such as nonlinear Rayleigh waves in elasticity.

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4

Song, Jiecheng, and Merry Ma. "Climate Change: Linear and Nonlinear Causality Analysis." Stats 6, no. 2 (2023): 626–42. http://dx.doi.org/10.3390/stats6020040.

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The goal of this study is to detect linear and nonlinear causal pathways toward climate change as measured by changes in global mean surface temperature and global mean sea level over time using a data-based approach in contrast to the traditional physics-based models. Monthly data on potential climate change causal factors, including greenhouse gas concentrations, sunspot numbers, humidity, ice sheets mass, and sea ice coverage, from January 2003 to December 2021, have been utilized in the analysis. We first applied the vector autoregressive model (VAR) and Granger causality test to gauge the

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5

Ibrahim, E. A., and S. P. Lin. "Weakly Nonlinear Instability of a Liquid Jet in a Viscous Gas." Journal of Applied Mechanics 59, no. 2S (1992): S291—S296. http://dx.doi.org/10.1115/1.2899503.

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The weakly nonlinear instability of a viscous liquid jet emanated into a viscous gas contained in a coaxial vertical circular pipe is investigated as an initial-value problem. The linear stability theory predicted that the jet may become unstable either due to capillary pinching or due to interfacial stress fluctuation. The results of nonlinear stability analysis shows no tendency of supercritical stability for both of the linearly unstable modes. In fact, the nonlinear growth rate of the disturbance is faster than the exponential growth rate of the linear normal mode disturbance for the same

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6

Spagnolo, Sergio, and Giovanni Taglialatela. "Analytic Propagation for Nonlinear Weakly Hyperbolic Systems." Communications in Partial Differential Equations 35, no. 12 (2010): 2123–63. http://dx.doi.org/10.1080/03605300903440490.

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7

Christianson, Hans, Jeremy Marzuola, Jason Metcalfe, and Michael Taylor. "Nonlinear Bound States on Weakly Homogeneous Spaces." Communications in Partial Differential Equations 39, no. 1 (2013): 34–97. http://dx.doi.org/10.1080/03605302.2013.845044.

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8

Rodriguez, Jesús, and Padraic Taylor. "Weakly nonlinear discrete multipoint boundary value problems." Journal of Mathematical Analysis and Applications 329, no. 1 (2007): 77–91. http://dx.doi.org/10.1016/j.jmaa.2006.06.024.

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9

Demenchuk, A. K. "Weakly irregular quasiperiodic solutions of nonlinear Pfaff systems." Differential Equations 44, no. 2 (2008): 186–91. http://dx.doi.org/10.1134/s0012266108020055.

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10

Dieter, Sabine. "Nonlinear degenerate curvature flows for weakly convex hypersurfaces." Calculus of Variations 22, no. 2 (2005): 229–51. http://dx.doi.org/10.1007/s00526-004-0279-4.

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11

Ostadzadeh, S. R., M. Salehi, and B. Jafari. "Efficient Analysis of Infinite Arrays of Nonlinear Antennas in the Frequency Domain." Advanced Electromagnetics 11, no. 2 (2022): 28–36. http://dx.doi.org/10.7716/aem.v11i2.1844.

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In this paper, different arrangements of infinite arrays of nonlinearly loaded antennas are analyzed in the frequency domain by an efficient approximate method and compared with the exact one with the aim of validity. The approximate method is based on the nonlinear current approach, while the second one is based on the harmonic balance. In one hand, although the harmonic balance technique is suitable for strongly nonlinear load, it is suffering from gradient operation and initial guess in the iteration process especially under multi tone excitations. On the other hand, although the approximat

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12

Xu, Run. "Some new nonlinear weakly singular integral inequalities and their applications." Journal of Mathematical Inequalities, no. 4 (2017): 1007–18. http://dx.doi.org/10.7153/jmi-2017-11-76.

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13

Taghipour, M., and H. Aminikhah. "Pell Collocation Method for Solving the Nonlinear Time–Fractional Partial Integro–Differential Equation with a Weakly Singular Kernel." Journal of Function Spaces 2022 (May 23, 2022): 1–15. http://dx.doi.org/10.1155/2022/8063888.

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This article focuses on finding the numerical solution of the nonlinear time–fractional partial integro–differential equation. For this purpose, we use the operational matrices based on Pell polynomials to approximate fractional Caputo derivative, nonlinear, and integro–differential terms; and by collocation points, we transform the problem to a system of nonlinear equations. This nonlinear system can be solved by the fsolve command in Matlab. The method’s stability and convergence have been studied. Also included are five numerical examples to demonstrate the veracity of the suggested strateg

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14

FEDDERSEN, FALK. "Weakly nonlinear shear waves." Journal of Fluid Mechanics 372 (October 10, 1998): 71–91. http://dx.doi.org/10.1017/s0022112098002158.

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Alongshore propagating low-frequency O(0.01 Hz) waves related to the direction and intensity of the alongshore current were first observed in the surf zone by Oltman-Shay, Howd & Birkemeier (1989). Based on a linear stability analysis, Bowen & Holman (1989) demonstrated that a shear instability of the alongshore current gives rise to alongshore propagating shear (vorticity) waves. The fully nonlinear dynamics of finite-amplitude shear waves, investigated numerically by Allen, Newberger & Holman (1996), depend on α, the non-dimensional ratio of frictional to nonlinear terms, essenti

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15

PORNPROMMIN, Adichai, Norihiro IZUMI, and Tetsuro TSUJIMOTO. "WEAKLY NONLINEAR ANALYSIS OF MULTIMODAL FLUVIAL BARS." PROCEEDINGS OF HYDRAULIC ENGINEERING 48 (2004): 1009–14. http://dx.doi.org/10.2208/prohe.48.1009.

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16

Ji, Zhen-Gang, and Cesar Mendoza. "Weakly Nonlinear Stability Analysis for Dune Formation." Journal of Hydraulic Engineering 123, no. 11 (1997): 979–85. http://dx.doi.org/10.1061/(asce)0733-9429(1997)123:11(979).

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17

Gross, L. K., and V. A. Volpert. "Weakly Nonlinear Stability Analysis of Frontal Polymerization." Studies in Applied Mathematics 110, no. 4 (2003): 351–75. http://dx.doi.org/10.1111/1467-9590.00242.

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18

Gérard-varet, D. "Weakly nonlinear analysis of the α effect". Geophysical & Astrophysical Fluid Dynamics 101, № 3-4 (2007): 171–84. http://dx.doi.org/10.1080/03091920701472535.

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19

Rigas, Georgios, Aimee S. Morgans, and Jonathan F. Morrison. "Weakly nonlinear modelling of a forced turbulent axisymmetric wake." Journal of Fluid Mechanics 814 (February 9, 2017): 570–91. http://dx.doi.org/10.1017/jfm.2017.32.

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A theory is presented where the weakly nonlinear analysis of laminar globally unstable flows in the presence of external forcing is extended to the turbulent regime. The analysis is demonstrated and validated using experimental results of an axisymmetric bluff-body wake at high Reynolds numbers, $Re_{D}\sim 1.88\times 10^{5}$, where forcing is applied using a zero-net-mass-flux actuator located at the base of the blunt body. In this study we focus on the response of antisymmetric coherent structures with azimuthal wavenumbers $m=\pm 1$ at a frequency $St_{D}=0.2$, responsible for global vortex

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20

Moreno-Pulido, Soledad, Francisco Javier García-Pacheco, Alberto Sánchez-Alzola, and Alejandro Rincón-Casado. "Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations." Mathematics 9, no. 9 (2021): 1036. http://dx.doi.org/10.3390/math9091036.

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There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where the nonlinear terms are “small” compared to the linear ones): the Method of Strained Parameters, the Naive Singular Perturbation Method, the Method of Multiple Scales, the Method of Harmonic Balance and the Method of Averaging. The Straightforward Expansion Perturbation Method (SEPM) applied to weakly nonlinear vibrations does not usually yield to correct solutions. In this manuscript, we provide mathematical proof of the inaccuracy of the SEPM in general cases. Nevertheless, we

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21

Goubet, Olivier, and Marilena Poulou. "Semi discrete weakly damped nonlinear Klein-Gordon Schrödinger system." Communications on Pure and Applied Analysis 13, no. 4 (2014): 1525–39. http://dx.doi.org/10.3934/cpaa.2014.13.1525.

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22

Boichuk, A., J. Diblík, D. Khusainov, and M. Růžičková. "Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems." Abstract and Applied Analysis 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/631412.

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Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems ofnordinary differential equations with constant coefficients and single delay (in the linear part) and with a finite number of measurable delays of argument in nonlinearity:ż(t)=Az(t-τ)+g(t)+εZ(z(hi(t),t,ε), t∈[a,b], assuming that these solutions satisfy the initial and boundary conditionsz(s):=ψ(s) if s∉[a,b], lz(⋅)=α∈Rm. The use of a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to anexplicitandanalyticalform of sufficient conditions for the existen

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23

Goubet, O., and L. Molinet. "Global attractor for weakly damped nonlinear Schrödinger equations in." Nonlinear Analysis: Theory, Methods & Applications 71, no. 1-2 (2009): 317–20. http://dx.doi.org/10.1016/j.na.2008.10.078.

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24

Srinivasan, Gopala Krishna, and V. D. Sharma. "On weakly nonlinear waves in media exhibiting mixed nonlinearity." Journal of Mathematical Analysis and Applications 285, no. 2 (2003): 629–41. http://dx.doi.org/10.1016/s0022-247x(03)00452-9.

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25

Carles, Rémi, Eric Dumas, and Christof Sparber. "Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations." SIAM Journal on Mathematical Analysis 42, no. 1 (2010): 489–518. http://dx.doi.org/10.1137/090750871.

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26

Gonçalves, Patrícia, and Milton Jara. "Nonlinear Fluctuations of Weakly Asymmetric Interacting Particle Systems." Archive for Rational Mechanics and Analysis 212, no. 2 (2013): 597–644. http://dx.doi.org/10.1007/s00205-013-0693-x.

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27

Ali, Usman, Haifa A. Alyousef, Umar Ishtiaq, Khalil Ahmed, and Shajib Ali. "Solving Nonlinear Fractional Differential Equations for Contractive and Weakly Compatible Mappings in Neutrosophic Metric Spaces." Journal of Function Spaces 2022 (March 21, 2022): 1–19. http://dx.doi.org/10.1155/2022/1491683.

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In this article, we aim to prove various unique fixed point results for contractive and weakly compatible mappings in the sense of neutrosophic metric spaces. Several nontrivial examples are also imparted. To support main result, uniqueness of solution of nonlinear fractional differential equations is examined.

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28

Zeng, Biao. "Optimal control for elliptic hemivariational inequalities involving nonlinear weakly continuous operators." Journal of Mathematical Inequalities, no. 2 (2021): 575–90. http://dx.doi.org/10.7153/jmi-2021-15-42.

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29

Pedas, Arvet. "POLYNOMIAL SPLINE COLLOCATION METHOD FOR NONLINEAR TWO‐DIMENSIONAL WEAKLY SINGULAR INTEGRAL EQUATIONS." Mathematical Modelling and Analysis 2, no. 1 (1997): 122–29. http://dx.doi.org/10.3846/13926292.1997.9637075.

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30

Orchini, Alessandro, Georgios Rigas, and Matthew P. Juniper. "Weakly nonlinear analysis of thermoacoustic bifurcations in the Rijke tube." Journal of Fluid Mechanics 805 (September 22, 2016): 523–50. http://dx.doi.org/10.1017/jfm.2016.585.

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In this study we present a theoretical weakly nonlinear framework for the prediction of thermoacoustic oscillations close to Hopf bifurcations. We demonstrate the method for a thermoacoustic network that describes the dynamics of an electrically heated Rijke tube. We solve the weakly nonlinear equations order by order, discuss their contribution on the overall dynamics and show how solvability conditions at odd orders give rise to Stuart–Landau equations. These equations, combined together, describe the nonlinear dynamical evolution of the oscillations’ amplitude and their frequency. Because w

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31

Pedas, Arvet, and Gennadi Vainikko. "The Smoothness of Solutions to Nonlinear Weakly Singular Integral Equations." Zeitschrift für Analysis und ihre Anwendungen 13, no. 3 (1994): 463–76. http://dx.doi.org/10.4171/zaa/501.

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32

vom Scheidt, J., S. Mehlhose, and R. Wunderlich. "Distribution Approximations for Nonlinear Functionals of Weakly Correlated Random Processes." Zeitschrift für Analysis und ihre Anwendungen 16, no. 1 (1997): 201–16. http://dx.doi.org/10.4171/zaa/759.

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33

WATANABE, Yasuharu. "WEAKLY NONLINEAR ANALYSIS OF BAR MODE REDUCTION PROCESS." PROCEEDINGS OF HYDRAULIC ENGINEERING 50 (2006): 967–72. http://dx.doi.org/10.2208/prohe.50.967.

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34

Rodrigues, Savio B., and Jayme De Luca. "Weakly nonlinear analysis of short-wave elliptical instability." Physics of Fluids 21, no. 1 (2009): 014108. http://dx.doi.org/10.1063/1.3068188.

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35

Wang, L. F., W. H. Ye, Z. F. Fan, Y. J. Li, X. T. He, and M. Y. Yu. "Weakly nonlinear analysis on the Kelvin-Helmholtz instability." EPL (Europhysics Letters) 86, no. 1 (2009): 15002. http://dx.doi.org/10.1209/0295-5075/86/15002.

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36

ALEXAKIS, ALEXANDROS, YUAN-NAN YOUNG, and ROBERT ROSNER. "Weakly nonlinear analysis of wind-driven gravity waves." Journal of Fluid Mechanics 503 (March 25, 2004): 171–200. http://dx.doi.org/10.1017/s0022112003007699.

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37

Wang, L. F., W. H. Ye, Z. F. Fan, Y. J. Li, X. T. He, and M. Y. Yu. "Weakly nonlinear analysis on the Kelvin-Helmholtz instability." EPL (Europhysics Letters) 87, no. 6 (2009): 69901. http://dx.doi.org/10.1209/0295-5075/87/69901.

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38

Graf, Tobias, Jerome Moloney, and Shankar Venkataramani. "Asymptotic analysis of weakly nonlinear Bessel–Gauß beams." Physica D: Nonlinear Phenomena 243, no. 1 (2013): 32–44. http://dx.doi.org/10.1016/j.physd.2012.09.004.

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39

Gupta, Karan, and Paresh Chokshi. "Weakly nonlinear stability analysis of polymer fibre spinning." Journal of Fluid Mechanics 776 (July 8, 2015): 268–89. http://dx.doi.org/10.1017/jfm.2015.284.

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The extensional flow of a polymeric fluid during the fibre spinning process is studied for finite-amplitude stability behaviour. The spinning flow is assumed to be inertialess and isothermal. The nonlinear extensional rheology of the polymer is described with the help of the eXtended Pom-Pom (XXP) model, which is known to exhibit a significant strain hardening effect necessary for fibre spinning applications. The linear stability analysis predicts an instability known as draw resonance when the draw ratio, $\mathit{DR}$, defined as the ratio of the velocities at the two ends of the fibre in th

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40

Chen, Feng. "Asymptotic analysis of weakly nonlinear and forced oscillations." Journal of Central South University of Technology 3, no. 2 (1996): 191–95. http://dx.doi.org/10.1007/bf02652203.

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41

Nadeem, Muhammad, and Hanan A. Wahash. "Analysis of Fractional Kundu-Eckhaus and Massive Thirring Equations Using a Hybridization Scheme." Journal of Function Spaces 2023 (March 28, 2023): 1–7. http://dx.doi.org/10.1155/2023/6704537.

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This paper deals with the study of fractional Kundu-Eckhaus equation (FKEE) and fractional massive Thirring problem (FMTP) that appear in the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. Since the variational iteration method involves integration, the Laplace transform involves convolution theorem in recurrence relation to derive the series solution. To avoid some assumptions and hypothesis, we apply a two-scale approach for such a nonlinear complex model. The fractional differential equation may be transformed into its partner equation using He’s fracti

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42

Goubet, Olivier. "Asymptotic Smoothing Effect for a Weakly Damped Nonlinear Schrodinger Equation in T2." Journal of Differential Equations 165, no. 1 (2000): 96–122. http://dx.doi.org/10.1006/jdeq.2000.3763.

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43

CLAVIN, PAUL. "SELF-SUSTAINED MEAN STREAMING MOTION IN DIAMOND PATTERNS OF A GASEOUS DETONATION." International Journal of Bifurcation and Chaos 12, no. 11 (2002): 2535–46. http://dx.doi.org/10.1142/s0218127402006060.

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A weakly nonlinear analysis of an overdriven detonation is carried out in the neighborhood of the instability threshold. The result leads to a nonlinear integral-differential equation describing the dynamics of the cellular front and exhibiting "diamond" patterns similar to those observed in experiments. An unexpected outcome of the analysis is a self-sustained mean streaming motion associated with the nonlinear dynamics of a weakly unstable detonation front.

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44

Krichen, Bilel, and Donal O'Regan. "On the class of relatively weakly demicompact nonlinear operators." Fixed Point Theory 19, no. 2 (2018): 625–30. http://dx.doi.org/10.24193/fpt-ro.2018.2.49.

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45

Benzoni-Gavage, Sylvie, and Jean-François Coulombel. "On the Amplitude Equations for Weakly Nonlinear Surface Waves." Archive for Rational Mechanics and Analysis 205, no. 3 (2012): 871–925. http://dx.doi.org/10.1007/s00205-012-0522-7.

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46

de Suzzoni, Anne-Sophie, and Nikolay Tzvetkov. "On the Propagation of Weakly Nonlinear Random Dispersive Waves." Archive for Rational Mechanics and Analysis 212, no. 3 (2014): 849–74. http://dx.doi.org/10.1007/s00205-014-0728-y.

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47

Shi, Xiulian, Yunxia Wei, and Fenglin Huang. "Spectral collocation methods for nonlinear weakly singular Volterra integro-differential equations." Numerical Methods for Partial Differential Equations 35, no. 2 (2018): 576–96. http://dx.doi.org/10.1002/num.22314.

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48

Deng, Guo, Christopher J. Lustri, and Mason A. Porter. "Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains." SIAM Journal on Applied Dynamical Systems 20, no. 4 (2021): 2412–49. http://dx.doi.org/10.1137/21m1398410.

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49

Shukla, Rahul, and Andrzej Wiśnicki. "Iterative methods for monotone nonexpansive mappings in uniformly convex spaces." Advances in Nonlinear Analysis 10, no. 1 (2021): 1061–70. http://dx.doi.org/10.1515/anona-2020-0170.

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Abstract We show the nonlinear ergodic theorem for monotone 1-Lipschitz mappings in uniformly convex spaces: if C is a bounded closed convex subset of an ordered uniformly convex space (X, ∣·∣, ⪯), T:C → C a monotone 1-Lipschitz mapping and x ⪯ T(x), then the sequence of averages 1 n ∑ i = 0 n − 1 T i ( x ) $ \frac{1}{n}\sum\nolimits_{i=0}^{n-1}T^{i}(x) $ converges weakly to a fixed point of T. As a consequence, it is shown that the sequence of Picard’s iteration {T n (x)} also converges weakly to a fixed point of T. The results are new even in a Hilbert space. The Krasnosel’skiĭ-Mann and the

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50

Čiegis, Raimondas, and Violeta Pakenienė. "Numerical Approximation of The Weakly Damped Nonlinear Schrödinger Equation." Computational Methods in Applied Mathematics 1, no. 4 (2001): 319–32. http://dx.doi.org/10.2478/cmam-2001-0021.

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AbstractIn this paper we consider the one-dimensional nonlinear Schrödinger equation. The equation includes an absorption term, and the solution is periodically amplified in order to compensate the lose of the energy. The problem describes propa- gation of a signal in optical fibers. In our previous work we proved that the well-known Crank—Nicolson scheme is unconditionally unstable for this problem. We present in this paper two finite difference approximations. The first one is given by a modified Crank—Nicolson scheme and the second one is obtained by a splitting scheme. The stability and co

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