Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure [PDF]
Studies in applied mathematics (Cambridge), 2019 The nonlinear Schrödinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude-frequency domains.
Congy, Thibault +3 more
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Soliton: A dispersion-less solution with existence and its types [PDF]
Heliyon, 2022 A solitary wave is the dispersion-less solution of nonlinear evolutionary equations that travels at a constant speed without dissipating its energy. The purpose of this article is to provide insight into the discovery and history of solitons.
Geeta Arora, Richa Rani, Homan Emadifar
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Impact of Brownian motion on the optical soliton solutions for the three component nonlinear Schrödinger equation [PDF]
Scientific ReportsIn this manuscript, the three-component nonlinear stochastic Schrö dinger equation under the effects of Brownian motion in the Stratonovich sense is examined here.
Muhammad Zafarullah Baber +5 more
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Scientific ReportsIn this study, the modified Sardar sub-equation method is capitalised to secure soliton solutions to the $$(1+1)$$ ( 1 + 1 ) -dimensional chiral nonlinear Schrödinger (NLS) equation.
Badr Saad T. Alkahtani
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Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings [PDF]
EntropyThis article presents a concise survey of basic discrete and semi-discrete nonlinear models, which produce two- and three-dimensional (2D and 3D) solitons, and a summary of the main theoretical and experimental results obtained for such solitons.
Boris A. Malomed
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Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations. [PDF]
Chaos, 2022 In this paper, using the algorithm due to Ablowitz et al. [Phys. Rev. Lett. 128, 184101 (2022); J. Phys. A: Math. Gen. 55, 384010 (2022)], we explore the anomalous dispersive relations, inverse scattering transform, and fractional N-soliton solutions of ...
Weifang Weng +3 more
semanticscholar +1 more source
Exp-function Method and Reduction Transformations for Rogue Wave Solutions of the Davey-Stewartson Equations [PDF]
Journal of Applied and Computational Mechanics, 2021 A pair of rogue wave solutions of the Davey-Stewartson (DS) equations are obtained by using the exp-function method and reduction transformations. Firstly, the Davey-Stewartson equations are transformed into two easy-to-solve equations, one of which is ...
Sheng Zhang, Yue Zhang, Bo Xu
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Shape-morphing reduced-order models for nonlinear Schrödinger equations [PDF]
Nonlinear dynamics, 2022 We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrödinger (NLS) equations. We compare two nonlinear reduced-order modeling methods: (i) The reduced Lagrangian approach which relies on the variational ...
W. Anderson, M. Farazmand
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Averaging of dispersion managed nonlinear Schrödinger equations [PDF]
Nonlinearity, 2021 We consider the dispersion managed power-law nonlinear Schrödinger (DM NLS) equations with a small parameter ɛ > 0 and the averaged equation, which are used in optical fiber communications.
Mi-Ran Choi, Young-Ran Lee
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Rational soliton solutions of nonlocal multicomponent nonlinear Schrödinger equations
Partial Differential Equations in Applied Mathematics, 2022 In this paper, we present a generalized Darboux transformation for nonlocal multicomponent nonlinear Schrödinger (NLS) equations. Also, we provide a unified formula for Nth-order rational soliton solution of discussed nonlocal multicomponent NLS ...
Li-Na Zheng, Yu-Shan Bai
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