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Journal articles on the topic 'Multi-Mode non-Linear Schrödinger equation'

Author: Grafiati

Published: 26 October 2024

Last updated: 30 July 2025

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1

BOGOLUBOV, N. N., M. Yu. RASULOVA, and I. A. TISHABOEV. "QUANTUM DYNAMICS OF TWO-LEVEL ATOMS INTERACTING WITH AN ELECTROMAGNETIC FIELD." International Journal of Modern Physics B 28, no. 08 (2014): 1450060. http://dx.doi.org/10.1142/s021797921450060x.

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We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation (GKE) is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrödinger equation, respectively.

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2

Misra, Shikha, Sanjay K. Mishra, and P. Brijesh. "Coaxial propagation of Laguerre–Gaussian (LG) and Gaussian beams in a plasma." Laser and Particle Beams 33, no. 1 (2015): 123–33. http://dx.doi.org/10.1017/s0263034615000142.

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AbstractThis paper investigates the non-linear coaxial (or coupled mode) propagation of Laguerre–Gaussian (LG) (in particular L01 mode) and Gaussian electromagnetic (em) beams in a homogeneous plasma characterized by ponderomotive and relativistic non-linearities. The formulation is based on numerical solution of non-linear Schrödinger wave equation under Jeffreys–Wentzel–Kramers–Brillouin approximation, followed by paraxial approach applicable in the vicinity of intensity maximum of the beams. A set of coupled differential equations for spot size (beam width) and phase evolution with space co

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3

Sakhabutdinov, Airat Zh, Vladimir I. Anfinogentov, Oleg G. Morozov, et al. "Numerical Method for Coupled Nonlinear Schrödinger Equations in Few-Mode Fiber." Fibers 9, no. 1 (2021): 1. http://dx.doi.org/10.3390/fib9010001.

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This paper discusses novel approaches to the numerical integration of the coupled nonlinear Schrödinger equations system for few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes’ interactions. In this case, the coupled nonlinear Schrödinger equation system (CNSES) solving becomes increasingly complex, because each mode affects the propa

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Zhu, Junyan, Jiang Cao, Chen Song, Bo Li, and Zhengsheng Han. "Numerical investigation on the convergence of self-consistent Schrödinger-Poisson equations in semiconductor device transport simulation." Nanotechnology 35, no. 31 (2024): 315001. http://dx.doi.org/10.1088/1361-6528/ad4558.

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Abstract Semiconductor devices at the nanoscale with low-dimensional materials as channels exhibit quantum transport characteristics, thereby their electrical simulation relies on the self-consistent solution of the Schrödinger-Poisson equations. While the non-equilibrium Green’s function (NEGF) method is widely used for solving this quantum many-body problem, its high computational cost and convergence challenges with the Poisson equation significantly limit its applicability. In this study, we investigate the stability of the NEGF method coupled with various forms of the Poisson equation, en

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Dabas, Bhawana, Jivesh Kaushal, Monika Rajput, and R. K. Sinha. "Study of Self Phase Modulation in Chalcogenide Glass Photonic Crystal Fiber." Applied Mechanics and Materials 110-116 (October 2011): 53–56. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.53.

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In this paper, Self Phase Modulation (SPM) in chalcogenide As2Se3glass Photonic Crystal Fiber (PCF) is numerically studied by combining the fully vectorial effective index method (FVEIM) and Split Step Fourier Method (SSFM). The FVEIM is used to calculate the variation of effective refractive index of guided mode (neff), effective area (Aeff), dispersion and non-linear coefficient (γ) with wavelength for different designs of chalcogenide As2Se3PCF. The FVEIM solves the vector wave equations and SSFM solves non linear Schrödinger Equation (NLSE) for the different designing parameter of As2Se3PC

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Niedda, Jacopo, Luca Leuzzi, and Giacomo Gradenigo. "Intensity pseudo-localized phase in the glassy random laser." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 5 (2023): 053302. http://dx.doi.org/10.1088/1742-5468/acd2c4.

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Abstract Evidence of an emergent pseudo-localized phase characterizing the low-temperature replica symmetry breaking phase of the complex disordered models for glassy light is provided in the mode-locked random laser model. A pseudo-localized phase corresponds to a state in which the intensity of light modes is neither equipartited among all modes nor strictly condensed on few of them. Such a hybrid phase, recently characterized as a finite size effect in other models, such as the discrete non-linear Schrödinger equation, in the low temperature phase of the glassy random laser appears to be ro

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Jahan, Sharmin, Rubaiya Khondoker Shikha, Abdul Mannan, and A. A. Mamun. "Modulational Instability of Ion-Acoustic Waves in Pair-Ion Plasma." Plasma 5, no. 1 (2021): 1–11. http://dx.doi.org/10.3390/plasma5010001.

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The modulational instability (MI) of ion-acoustic waves (IAWs) is examined theoretically in a four-component plasma system containing inertialess electrons featuring a non-thermal, non-extensive distribution, iso-thermal positrons, and positively as well as negatively charged inertial ions. In this connection, a non-linear Schrödinger equation (NLSE), which dominates the conditions for MI associated with IAWs, is obtained by using the reductive perturbation method. The numerical analysis of the NLSE reveals that the increment in non-thermality leads to a more unstable state, whereas the enhanc

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8

Odegov, N. A., and I. S. Baleyev. "A NUMERICAL-ANALYTICAL METHOD FOR THE SYNTHESIS OF OPTIMAL IRREGULAR DWDM FREQUENCY PLANS." Proceedings of the O.S. Popov ОNAT 1, no. 2 (2020): 70–81. http://dx.doi.org/10.33243/2518-7139-2020-1-2-70-81.

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The possibilities of increasing the throughput of fiber-optic transmission systems by using an uneven frequency grid are investigated. In this case, the bandwidth of each channel is selected so that the transmission rate is the same for all channels. In this work, both linear and some nonlinear effects are taken into account, leading to the distortion of the optical pulse. Simulation of nonlinear effects is based on a model in the form of a generalized nonlinear Schrödinger equation. The developed program provides modeling of linear and nonlinear distortions for the DWDM range (from 1460 to 16

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REZNIK, G. M., V. ZEITLIN, and M. BEN JELLOUL. "Nonlinear theory of geostrophic adjustment. Part 1. Rotating shallow-water model." Journal of Fluid Mechanics 445 (October 16, 2001): 93–120. http://dx.doi.org/10.1017/s002211200100550x.

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We develop a theory of nonlinear geostrophic adjustment of arbitrary localized (i.e. finite-energy) disturbances in the framework of the non-dissipative rotating shallow-water dynamics. The only assumptions made are the well-defined scale of disturbance and the smallness of the Rossby number Ro. By systematically using the multi-time-scale perturbation expansions in Rossby number it is shown that the resulting field is split in a unique way into slow and fast components evolving with characteristic time scales f−10 and (f0Ro)−1 respectively, where f0 is the Coriolis parameter. The slow compone

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Muhammad, Zahid, Ubaid Ullah Khalil, Anees Khan, Tanweer Ahmed, Waqas Khan, and Samra Naz. "Design Optimization of Fiber Laser for Generation of Femtosecond Optical Pulses." Scholars Journal of Physics, Mathematics and Statistics 11, no. 08 (2024): 89–100. http://dx.doi.org/10.36347/sjpms.2024.v11i08.002.

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The precise coordination of dispersion management, temperature control, mode-locking mechanisms, and gain medium qualities are required in the design and optimization of fiber laser cavities for the generation of femtosecond pulses. The performance and capacities of femtosecond fiber lasers are being enhanced by developments in these fields, opening up new uses for them. The main focus of this research work was to design a lasing cavity for the generation of femtosecond optical pulses. So, we designed a laser cavity having six segments with a total length of 5.4 meters. The first segment is a

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Dias, João-Paulo. "Linear stability of shock profiles for a quasilinear Benney system in ℝ2 × ℝ+". Journal of Hyperbolic Differential Equations 17, № 04 (2020): 797–807. http://dx.doi.org/10.1142/s0219891620500253.

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Following Dias et al. [Vanishing viscosity with short wave-long wave interactions for multi-D scalar conservation laws, J. Differential Equations 251 (2007) 555–563], we study the linearized stability of a pair [Formula: see text], where [Formula: see text] is a shock profile for a family of quasilinear hyperbolic conservation laws in [Formula: see text] coupled with a semilinear Schrödinger equation.

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12

Cole, Eric A. B., Tobias Boettcher, and Christopher M. Snowden. "Two-dimensional Modelling of HEMTs Using Multigrids with Quantum Correction." VLSI Design 8, no. 1-4 (1998): 29–34. http://dx.doi.org/10.1155/1998/61608.

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The two-dimensional multi-layered HEMT is modelled isothermally by solving the Poisson and current continuity equations consistently with the Schrödinger equation. A multigrid method is used on the Poisson and current continuity equations while the electron density is calculated at each level by solving the Schrödinger equation in onedimensional slices perpendicular to the layer structure. A correction factor is introduced which enables relatively accurate solutions to be obtained using a low number of eigensolutions. A novel method for discretising the current density which can be generalised

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13

Fagnola, Franco, and Carlos M. Mora. "Basic Properties of a Mean Field Laser Equation." Open Systems & Information Dynamics 26, no. 03 (2019): 1950015. http://dx.doi.org/10.1142/s123016121950015x.

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We study the nonlinear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the nonlinear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schrödinger equation. To this end, we find a regular solution for the nonautonomous linear quantum master equation in Gorini–Kossakowski–Sudarshan–Lind

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14

García-Muñoz, Juan D., Julio Cesar Pérez-Pedraza, and A. Raya. "Dirac materials in parallel electromagnetic fields generated by supersymmetry." Journal of Physics: Conference Series 2667, no. 1 (2023): 012053. http://dx.doi.org/10.1088/1742-6596/2667/1/012053.

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Abstract In a Supersymetric Quantum Mechanics framework, the Dirac equation describing a Dirac material in the presence of electromagnetic fields is solved. Considering parallel static non-uniform electromagnetic fields, the Dirac equation is transformed into a two-dimensional system of equations. By means of variable separation, we can define one-dimensional eigenfunctions, which are solutions for two pairs of supersymmetric partner Schrödinger-like Hamiltonians. For Pöschl-Teller-like quantum potentials, we look for conditions that guarantee the existence of bound states, and determine an an

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15

Duffner, E., and A. Rieckers. "On the Global Quantum Dynamics of Multi- Lattice Systems with Non-linear Classical Effects." Zeitschrift für Naturforschung A 43, no. 6 (1988): 521–32. http://dx.doi.org/10.1515/zna-1988-0602.

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Abstract The microscopic dynamics for a class of long range interacting multi-lattice quantum systems is constructed in the thermodynamical limit by means of operator algebraic concepts. By direct estimations the existence of the limiting Schrödinger dynamics is proven for a set of states, which comprises also globally non-equilibrium situations. The expectation values of the classical observables in the pure phase states are shown to satisfy a set of coupled non-linear differential equations. The limiting Heisenberg dynamics is derived as a W*-automorphism group in the partially universal von

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16

Gao, T., Z. Wang, and P. A. Milewski. "Nonlinear hydroelastic waves on a linear shear current at finite depth." Journal of Fluid Mechanics 876 (July 31, 2019): 55–86. http://dx.doi.org/10.1017/jfm.2019.528.

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This work is concerned with waves propagating on water of finite depth with a constant-vorticity current under a deformable flexible sheet. The pressure exerted by the sheet is modelled by using the Cosserat thin shell theory. By means of multi-scale analysis, small amplitude nonlinear modulation equations in several regimes are considered, including the nonlinear Schrödinger equation (NLS) which is used to predict the existence of small-amplitude wavepacket solitary waves in the full Euler equations and to study the modulational instability of quasi-monochromatic wavetrains. Guided by these w

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17

Lill, Sascha, Lukas Nickel, and Roderich Tumulka. "Consistency Proof for Multi-time Schrödinger Equations with Particle Creation and Ultraviolet Cut-Off." Annales Henri Poincaré 22, no. 6 (2021): 1887–936. http://dx.doi.org/10.1007/s00023-020-01009-w.

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AbstractFor multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schrödinger equation consists of several equations, one for each time variable. This leads to the question of how to prove the consistency of such a system of PDEs. The question becomes more difficult for theories with particle creation, as then different sectors of the wave function have different numbers of time variables. Petrat and Tumulka (2014) gave an example of such a model and a non-rigorous argument for its consistency. We gi

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18

HACKENBERG, PETER, and GOTTFRIED MANN. "Parallel weak envelope solitons in multi-ion plasmas." Journal of Plasma Physics 61, no. 4 (1999): 633–44. http://dx.doi.org/10.1017/s0022377899007631.

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Heavy ions frequently appear as minor components in space plasmas, for example as charged helium in the solar wind and heavy ions in the vicinity of comets. Both the different components of ions and the associated plasma waves are observed by extraterrestrial in situ measurements. These plasma waves appear as large-amplitude magnetic field fluctuations in space plasmas. They must be described appropriately by means of multifluid equations. Because of the nonlinear nature of these waves, we here investigate nonlinear waves in multi-ion plasmas. Solitary waves that can only exist in a magnetized

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19

CHEN, XUE-NONG, and Rong-Jue Wei. "Dynamic behaviour of a non-propagating soliton under a periodically modulated oscillation." Journal of Fluid Mechanics 259 (January 25, 1994): 291–303. http://dx.doi.org/10.1017/s0022112094000145.

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It has been found theoretically and experimentally that a non-propagating soliton in a small rectangular water tank manifests dynamic behaviour when subjected to a modulated oscillation. A modification of the cubic Schrödinger equation was generalized for this case and analysed by the inverse-scattering perturbation method. The problem was reduced to a lower-dimensional one, i.e. to a pair of first-order ordinary differential equations for the amplitude and phase of the soliton, which were solved numerically. It was found that the soliton executes multi-periodic and chaotic motions under the p

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20

TANG, BING, DE-JUN LI, KE HU, and YI TANG. "INTRINSIC LOCALIZED MODES IN QUANTUM FERROMAGNETIC ISING–HEISENBERG CHAINS WITH SINGLE-ION UNIAXIAL ANISOTROPY." International Journal of Modern Physics B 27, no. 25 (2013): 1350139. http://dx.doi.org/10.1142/s0217979213501397.

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Based on the coherent-state method combined with the Dyson–Maleev representation of spin operators, the existence and properties of intrinsic localized spin-wave modes in quantum ferromagnetic Ising–Heisenberg chains with single-ion uniaxial anisotropy are investigated analytically in the semiclassical limit. With the help of the multiple-scale method combined with semidiscrete approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, a bright type intrinsic localized spin-wave

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21

Ghizdovat, Vlad, Oana Rusu, Mihail Frasila, Cristina Marcela Rusu, Maricel Agop, and Decebal Vasincu. "Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics." Entropy 25, no. 8 (2023): 1149. http://dx.doi.org/10.3390/e25081149.

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Some possible correspondences between the Scale Relativity Theory and the Space–Time Theory can be established. Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gravitational field with axial symmetry accept the same SL(2R)-type invariance, an Ernst-type potential (from General Relativity) and also a multi-fractal tensor (from Scale Relativity) are highlighted in the description of complex systems dynamics. In this way, a non-differentiable description of complex systems dynamics can become functional, even in the case

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22

Mousavi Lajimi, S. Amir, and Michael I. Friswell. "Energy harvesting from a non-linear standing beam–mass system: Two- versus one-mode approximations." Journal of Intelligent Material Systems and Structures 28, no. 8 (2016): 1010–22. http://dx.doi.org/10.1177/1045389x16667852.

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We investigate the effect of including the second mode of natural vibration on the computed response of a forced non-linear gravity-loaded beam–mass structure used for non-linear piezoelectric energy harvesting. Using the method of assumed-modes and Lagrange’s equations, we develop the discretized equations of generalized coordinates of the system including the electro-mechanical equation. The equation of motion is further simplified to find the single-mode approximation. The phase-portraits, time-histories, Poincaré sections, and frequency–response curves of the system are computed. It is sho

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23

Wang, Xiaoming, and Zhi-Qiang Wang. "Normalized multi-bump solutions for saturable Schrödinger equations." Advances in Nonlinear Analysis 9, no. 1 (2019): 1259–77. http://dx.doi.org/10.1515/anona-2020-0054.

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Abstract In this paper, we are concerned with the existence of multi-bump solutions for a class of semiclassical saturable Schrödinger equations with an density function: $$\begin{array}{} \displaystyle -{\it\Delta} v +{\it\Gamma} \frac{I(\varepsilon x) + v^2}{1+I(\varepsilon x) +v^2} v =\lambda v,\, x\in{{\mathbb{R}}^{2}}. \end{array}$$ We prove that, with the density function being radially symmetric, for given integer k ≥ 2 there exist a family of non-radial, k-bump type normalized solutions (i.e., with the L2 constraint) which concentrate at the global maximum points of density functions w

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24

Hanapi, Mohd Syafiq M., Abdel-Baset M. A. Ibrahim, Rafael Julius, and Hichem Eleuch. "Quantum Kerr nonlinear coupler: analytical versus phase-space method." Canadian Journal of Physics 99, no. 9 (2021): 832–40. http://dx.doi.org/10.1139/cjp-2020-0389.

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The generation of squeezed states of light in a two-mode Kerr nonlinear directional coupler (NLDC) was investigated using two different methods in quantum mechanics. First, the analytical method, a Heisenberg-picture-based method where the operators are evolving in time but the state vectors are time-independent. In this method, an analytical solution to the coupled Heisenberg equations of motion for the propagating modes was proposed based on the Baker–Hausdorff (BH) formula. Second, the phase space method, a Schrödinger-picture-based method in which the operators are constant and the density

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25

ESFANDYARI-KALEJAHI, A., I. KOURAKIS, and M. AKBARI-MOGHANJOUGHI. "Nonlinear modulation of ion-acoustic waves in two-electron-temperature plasmas." Journal of Plasma Physics 76, no. 2 (2010): 169–81. http://dx.doi.org/10.1017/s0022377810000024.

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AbstractThe amplitude modulation of ion-acoustic waves is investigated in a plasma consisting of adiabatic warm ions, and two different populations of thermal electrons at different temperatures. The fluid equations are reduced to nonlinear Schrödinger equation by employing a multi-scale perturbation technique. A linear stability analysis for the wave packet amplitude reveals that long wavelengths are always stable, while modulational instability sets in for shorter wavelengths. It is shown that increasing the value of the hot-to-cold electron temperature ratio (μ), for a given value of the ho

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WANG, ZHONGCHENG, and YONGMING DAI. "A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION." International Journal of Modern Physics C 14, no. 08 (2003): 1087–105. http://dx.doi.org/10.1142/s0129183103005194.

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A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

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27

Zhang, Yanwei, Xiong You, and Yonglei Fang. "Exponentially fitted multi-derivative linear methods for the resonant state of the Schrödinger equation." Journal of Mathematical Chemistry 55, no. 1 (2016): 223–37. http://dx.doi.org/10.1007/s10910-016-0683-y.

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Zhang, Yanwei, Yonglei Fang, Xiong You, and Guangde Liu. "Trigonometrically-fitted multi-derivative linear methods for the resonant state of the Schrödinger equation." Journal of Mathematical Chemistry 56, no. 4 (2017): 1250–61. http://dx.doi.org/10.1007/s10910-017-0851-8.

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29

Cao, Daomin, Shanfa Lai, and Weilin Yu. "Multi-peak solutions to the Schrödinger equations coupled with a neutral scalar field." Journal of Mathematical Physics 64, no. 2 (2023): 021510. http://dx.doi.org/10.1063/5.0121726.

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In this paper, we consider the problem of Schrödinger equation coupled with a neutral scalar field. By constructing solutions with multiple peaks, we prove that the number of non-radial solutions of this problem goes to infinity as the Maxwell coupling constant tends to infinity. The Chern–Simons limit of those solutions is also discussed.

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30

Stalin, S., R. Ramakrishnan, and M. Lakshmanan. "Nondegenerate Bright Solitons in Coupled Nonlinear Schrödinger Systems: Recent Developments on Optical Vector Solitons." Photonics 8, no. 7 (2021): 258. http://dx.doi.org/10.3390/photonics8070258.

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Nonlinear dynamics of an optical pulse or a beam continue to be one of the active areas of research in the field of optical solitons. Especially, in multi-mode fibers or fiber arrays and photorefractive materials, the vector solitons display rich nonlinear phenomena. Due to their fascinating and intriguing novel properties, the theory of optical vector solitons has been developed considerably both from theoretical and experimental points of view leading to soliton-based promising potential applications. Mathematically, the dynamics of vector solitons can be understood from the framework of the

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31

Paldor, Nathan, Yair De-Leon, and Ofer Shamir. "Planetary (Rossby) waves and inertia–gravity (Poincaré) waves in a barotropic ocean over a sphere." Journal of Fluid Mechanics 726 (May 30, 2013): 123–36. http://dx.doi.org/10.1017/jfm.2013.219.

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AbstractThe construction of approximate Schrödinger eigenvalue equations for planetary (Rossby) waves and for inertia–gravity (Poincaré) waves on an ocean-covered rotating sphere yields highly accurate estimates of the phase speeds and meridional variation of these waves. The results are applicable to fast rotating spheres such as Earth where the speed of barotropic gravity waves is smaller than twice the tangential speed on the equator of the rotating sphere. The implication of these new results is that the phase speed of Rossby waves in a barotropic ocean that covers an Earth-like planet is

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Cai, Hao, Feng-Ming Liu, and Nian-Ning Huang. "Dark Multi-Soliton Solution of the Nonlinear Schrödinger Equation with Non-Vanishing Boundary." International Journal of Theoretical Physics 44, no. 2 (2005): 255–65. http://dx.doi.org/10.1007/s10773-005-1691-z.

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Chen, Li-Qun, Hu Ding, and C. W. Lim. "Principal Parametric Resonance of Axially Accelerating Viscoelastic Beams: Multi-Scale Analysis and Differential Quadrature Verification." Shock and Vibration 19, no. 4 (2012): 527–43. http://dx.doi.org/10.1155/2012/948459.

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Transverse non-linear vibration is investigated in principal parametric resonance of an axially accelerating viscoelastic beam. The axial speed is characterized as a simple harmonic variation about a constant mean speed. The material time derivative is used in the viscoelastic constitutive relation. The transverse motion can be governed by a non-linear partial-differential equation or a non-linear integro-partial-differential equation. The method of multiple scales is applied to the governing equations to determine steady-state responses. It is confirmed that the mode uninvolved in the resonan

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Xu, Xice, Yang Lu, and Xufeng Wu. "Dynamic Modeling and Control Law Design of a Fuel-electric Hybrid Multi-rotor UAV." International Journal of Micro Air Vehicles 14 (January 2022): 175682932210789. http://dx.doi.org/10.1177/17568293221078925.

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In this paper, the design of control law for a new concept fuel-electric hybrid multi-rotor UAV with lift/attitude control separation is investigated. The remarkable feature of the UAV is that it has a large proportion of fuel weight. Firstly, based on the quasi-coordinate Lagrangian equation and sloshing equivalent model using the multi-mass-spring analogy, the non-linear dynamic model of the UAV considering the fuel slosh dynamics is established. Compared with the existing multi-rotor modeling method, it is more intuitive and accurate to describe the non-linear coupling process of sloshing a

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Zolotaryuk, Alexander V., and Yaroslav Zolotaryuk. "Conditions for realizing one-point interactions from a multi-layer structure model." Journal of Physics A: Mathematical and Theoretical 55, no. 8 (2022): 085201. http://dx.doi.org/10.1088/1751-8121/ac4a1f.

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Abstract A heterostructure composed of N parallel homogeneous layers is studied in the limit as their widths l 1, …, l N shrink to zero. The problem is investigated in one dimension and the piecewise constant potential in the Schrödinger equation is given by the strengths V 1, …, V N as functions of l 1, …, l N , respectively. The key point is the derivation of the conditions on the functions V 1(l 1), …, V N (l N ) for realizing a family of one-point interactions as l 1, …, l N tend to zero along available paths in the N-dimensional space. The existence of equations for a squeezed structure,

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BALA, PARVEEN, TARSEM SINGH GILL, and HARVINDER KAUR. "Ion-acoustic envelope excitations in multispecies plasma with non-thermally distributed electrons." Journal of Plasma Physics 78, no. 3 (2012): 265–78. http://dx.doi.org/10.1017/s0022377812000013.

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AbstractBy using the standard reductive perturbation technique, a nonlinear Schrödinger equation is derived to study the stability of finite amplitude ion-acoustic waves in an unmagnetized plasma consisting of warm positive and negative ions and non-thermal electrons. The effect of relative temperature of positive and negative ions, their charge and mass ratios, density ratios and non-thermally distributed electrons on modulational instability of fast and slow ion-acoustic mode is investigated. It is found that these parameters significantly change the domain of modulation instability. Both, e

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Caruso, Enrico, David Esseni, Elena Gnani, et al. "Modeling Nanoscale III–V Channel MOSFETs with the Self-Consistent Multi-Valley/Multi-Subband Monte Carlo Approach." Electronics 10, no. 20 (2021): 2472. http://dx.doi.org/10.3390/electronics10202472.

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We describe the multi-valley/multi-subband Monte Carlo (MV–MSMC) approach to model nanoscale MOSFETs featuring III–V semiconductors as channel material. This approach describes carrier quantization normal to the channel direction, solving the Schrödinger equation while off-equilibrium transport is captured by the multi-valley/multi-subband Boltzmann transport equation. In this paper, we outline a methodology to include quantum effects along the transport direction (namely, source-to-drain tunneling) and provide model verification by comparison with Non-Equilibrium Green’s Function results for

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Verheest, Frank, and B. Buti. "Parallel solitary Alfvén waves in warm multi-species beam-plasma systems. Part 1." Journal of Plasma Physics 47, no. 1 (1992): 15–24. http://dx.doi.org/10.1017/s0022377800024041.

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A self-consistent reductive perturbation analysis for parallel-propagating magnetohydrodynamic waves in warm multi-species plasmas, in which different constituents can have differing equilibrium drifts, leads to a derivative nonlinear Schrödinger equation for the wave magnetic field. Soliton solutions are discussed, including applications to plasmas with two ion species. Such solitons are larger (in amplitude) and wider than in the non-streaming and/or cold-plasma case, other parameters being equal.

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ISAR, A., A. SANDULESCU, H. SCUTARU, E. STEFANESCU, and W. SCHEID. "OPEN QUANTUM SYSTEMS." International Journal of Modern Physics E 03, no. 02 (1994): 635–714. http://dx.doi.org/10.1142/s0218301394000164.

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The damping of the harmonic oscillator is studied in the framework of the Lindblad theory for open quantum systems. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schrödinger, Heisenberg and Weyl-Wigner-Moyal representations of the Lindblad equation are given explicitly. On the basis of these representations it is shown that various master equations for the damped quantum oscillator used in the literature are particular cases of the Lindblad equation and that no

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40

Veklenko, Boris A. "Coherent Stimulated Radiation, Coherent Spontaneous Radiation and Coupled Photon Pairs in Non-Uniform Thermally Excited Gaseous Media: The Theory." Issue 01-2022, no. 01-2022 (February 2022): 4–11. http://dx.doi.org/10.33383/2021-099.

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It is demonstrated that presence of stimulated radiation processes in gaseous media makes it possible to generate rays inversely reflected from interfaces of thermally excited gaseous media and the processes of left-hand refraction of the rays having passed through these media. These processes are caused by availability of coupled photonic states and stimulated radiation in media the properties of which differ from those of stimulated radiation in vacuum. Estimation of these processes is based on exclusion of the procedure of forced breaking of quantum correlators and correct consideration of

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Broadbridge, Philip, and Kathryn Deutscher. "Solution of Non-Autonomous Schrödinger Equation for Quantized de Sitter Klein-Gordon Oscillator Modes Undergoing Attraction-Repulsion Transition." Symmetry 12, no. 6 (2020): 943. http://dx.doi.org/10.3390/sym12060943.

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For a scalar field in an exponentially expanding universe, constituent modes of elementary excitation become unstable consecutively at shorter wavelength. After canonical quantization, a Bogoliubov transformation reduces the minimally coupled scalar field to independent 1D modes of two inequivalent types, leading eventually to a cosmological partitioning of energy. Due to accelerated expansion of the coupled space-time, each underlying mode transits from an attractive oscillator with discrete energy spectrum to a repulsive unit with continuous unbounded energy spectrum. The underlying non-auto

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Abia Nonga, Régis Jean François, Adoukalt Chanceu, Wolfgang Nzie, and Guy Edgard Ntamack. "Dynamic Control of Piezoelectric Sandwich Beams with Multi-Frequency Excitations." American Journal of Innovation in Science and Engineering 3, no. 3 (2024): 69–76. http://dx.doi.org/10.54536/ajise.v3i3.2848.

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In this work, we present a non-linear analysis of the dynamics of a sandwich beam with piezoelectric patches under multi-frequency excitations. The model takes into account geometrical non-linearities, piezoelectric non-linearities, and inertia. Hamilton’s principle is used to determine the electromechanical equation of motion, and Garlekin’s technique is used to determine the equivalent model of the piezoelectric generator. A mathematical methodology based on the multi-scale method for vibration control and stability is reviewed in this work to determine a system of amplitude and phase equati

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Sergeyev, Sergey V. "Fast and slowly evolving vector solitons in mode-locked fibre lasers." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, no. 2027 (2014): 20140006. http://dx.doi.org/10.1098/rsta.2014.0006.

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We report on a new vector model of an erbium-doped fibre laser mode locked with carbon nanotubes. This model goes beyond the limitations of the previously used models based on either coupled nonlinear Schrödinger or Ginzburg–Landau equations. Unlike the previous models, it accounts for the vector nature of the interaction between an optical field and an erbium-doped active medium, slow relaxation dynamics of erbium ions, linear birefringence in a fibre, linear and circular birefringence of a laser cavity caused by in-cavity polarization controller and light-induced anisotropy caused by ellipti

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Yapanmış, Burak Emre, and Süleyman Murat Bağdatlı. "Investigation of the non-linear vibration behaviour and 3:1 internal resonance of the multi supported nanobeam." Zeitschrift für Naturforschung A 77, no. 4 (2021): 305–21. http://dx.doi.org/10.1515/zna-2021-0300.

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Abstract In this present work, linear and non-linear vibration of multi-supported nanobeams, which are a fundamental part of the nano-electromechanical systems, is examined. To the best of the researchers’ knowledge, there is no study performed into multi-supported nanobeam in the literature. The governing equations of the system are obtained by dint of the Hamilton principle and solved via the perturbation technique which is divided linear and non-linear parts of the main equations. The natural frequencies and mode shapes are calculated from the linear problem. The non-linear natural frequenc

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Ying, Zu-Guang, and Yi-Qing Ni. "Vibration Localization and Anti-Localization of Nonlinear Multi-Support Beams with Support Periodicity Defect." Symmetry 13, no. 12 (2021): 2234. http://dx.doi.org/10.3390/sym13122234.

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A response analysis method for nonlinear beams with spatial distribution parameters and non-periodic supports was developed. The proposed method is implemented in four steps: first, the nonlinear partial differential equation of the beams is transformed into linear partial differential equations with space-varying parameters by using a perturbation method; second, the space-varying parameters are separated into a periodic part and a non-periodic part describing the periodicity defect, and the linear partial differential equations are separated into equations for the periodic and non-periodic p

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Xia, Wei, Xinghong Zhao, Datao Li, and Shengping Shen. "Nonlinear flutter response of pre-heated functionally graded panels." International Journal of Computational Materials Science and Engineering 07, no. 01n02 (2018): 1850012. http://dx.doi.org/10.1142/s2047684118500124.

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The thermo-mechanical behavior of functionally graded (FG) panels is investigated in supersonic air flow. The three-node triangular element based on the Mindlin plate theory is employed to account for the transverse shear strains, and the von-Karman nonlinear strain–displacement relation is utilized considering the geometric nonlinearity. The effective material properties of the FG material are assumed to vary through the thickness according to simple power law distribution. The aeroelastic equation is established using the first-order piston theory, the linear rule of mixture and the principl

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Niu, Yahui, Shuying Tian, and Pingping Yang. "Local uniqueness of multi-peak solutions to a class of Schrödinger equations with competing potential." Journal of Mathematical Physics 64, no. 3 (2023): 031509. http://dx.doi.org/10.1063/5.0134220.

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In this paper, we consider the nonlinear Schrödinger equations. Let [Formula: see text]. Under some conditions on [Formula: see text], we show the local uniqueness of positive multi-peak solutions concentrating near k( k ≥ 2) distinct non-degenerate critical points of [Formula: see text] by using the local Pohozaev identity. We generalize Cao–Li–Luo’s results to the competing potential cases and show how these two potentials impact the uniqueness of concentrated solutions.

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Budaca, Radu, and Andreea-Ioana Budaca. "Spin dynamics of triaxial nuclei with a quasiparticle alignment." EPJ Web of Conferences 324 (2025): 00003. https://doi.org/10.1051/epjconf/202532400003.

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The dynamics of nuclei with a triaxial core and a non-axial rigid quasiparticle alignment is described with a Schrödinger equation constructed from a semiclassical formalism. The use of the total angular momentum projection as a continuous variable and the separation of the potential energy allows the interpretation of the spectra in terms of anharmonic wobbling oscillations and tilted axis rotations. The experimental realization of the model is presented for the h11/2 quasiparticle bands of the 133La nucleus, which is found to exhibit a novel tilted-axis wobbling mode of excitation.

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Yong, Xuelin, Yajing Fan, Yehui Huang, Wen-Xiu Ma, and Jing Tian. "Darboux transformation and solitons for an integrable nonautonomous nonlinear integro-differential Schrödinger equation." Modern Physics Letters B 31, no. 30 (2017): 1750276. http://dx.doi.org/10.1142/s0217984917502761.

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By modifying the scheme for an isospectral problem, the non-isospectral Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy is constructed via allowing the time varying spectrum. In this paper, we consider an integrable nonautonomous nonlinear integro-differential Schrödinger equation discussed before in “Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation” [Y. J. Zhang, D. Zhao and H. G. Luo, Ann. Phys. 350 (2014) 112]. We first analyze the integrability conditions and identify the model. Second, we modify the existing Darboux transformation (D

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Le Coz, Stefan, Dong Li, and Tai-Peng Tsai. "Fast-moving finite and infinite trains of solitons for nonlinear Schrödinger equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 6 (2015): 1251–82. http://dx.doi.org/10.1017/s030821051500030x.

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We study infinite soliton trains solutions of nonlinear Schrödinger equations, i.e. solutions behaving as the sum of infinitely many solitary waves at large time. Assuming the composing solitons have sufficiently large relative speeds, we prove the existence and uniqueness of such a soliton train. We also give a new construction of multi-solitons (i.e. finite trains) and prove uniqueness in an exponentially small neighbourhood, and we consider the case of solutions composed of several solitons and kinks (i.e. solutions with a non-zero background at infinity).

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