Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients [PDF]
Nuclear Physics B, 2023 The nonlinear Schrödinger (NLS) types of equations play a key role in quantum mechanics, Quantum communication and physical applications. However, how to deal with explicit solutions and other properties of the NLS equations, especially for the variable ...
Hanze Liu
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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
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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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