Exact Multisoliton Solutions of General Nonlinear Schrödinger Equation with Derivative [PDF]
The Scientific World Journal, 2014 Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota’s approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated.
Qi Li, Qiu-yuan Duan, Jian-bing Zhang
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The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method. [PDF]
Proc Math Phys Eng Sci, 2016 In this paper, we implement the Fokas method to study initial-boundary value problems of the mixed coupled nonlinear Schrödinger equation formulated on the half-line with Lax pairs involving 3×3 matrices.
Tian SF.
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Rogue periodic waves of the focusing nonlinear Schrödinger equation. [PDF]
Proc Math Phys Eng Sci, 2018 Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn.
Chen J, Pelinovsky DE.
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Novel soliton solutions and phase plane analysis in nonlinear Schrödinger equations with logarithmic nonlinearities [PDF]
Scientific ReportsThis paper investigates a generalized form of the nonlinear Schrödinger equation characterized by a logarithmic nonlinearity. The nonlinear Schrödinger equation, a fundamental equation in nonlinear wave theory, is applied across various physical systems ...
Du’a Al-zaleq, Lewa’ Alzaleq
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Bifurcation analysis of small amplitude unidirectional waves for nonlinear Schrödinger equations with fractional derivatives [PDF]
Scientific ReportsThis study explores bifurcation phenomena in the nonlinear time-dependent Schrödinger equation and related models, applying Kudryashov’s methods to find exact solutions.
Safoura Rezaei Aderyani +3 more
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Finite difference method for a nonlinear fractional Schrödinger equation with Neumann condition [PDF]
E-Journal of Analysis and Applied Mathematics, 2020 In this paper, a special case of nonlinear fractional Schrödinger equation with Neumann boundary condition is considered. Finite difference method is implemented to solve the nonlinear fractional Schrödinger problem with Neumann boundary condition ...
Betul Hicdurmaz
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Soliton, breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints [PDF]
Chinese Physics B, 2020 The nonlinear Schrödinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas.
Jun-Cai 俊才 Pu 蒲 +2 more
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Evolution of Water Wave Groups in the Forced Benney–Roskes System
Fluids, 2023 For weakly nonlinear waves in one space dimension, the nonlinear Schrödinger Equation is widely accepted as a canonical model for the evolution of wave groups described by modulation instability and its soliton and breather solutions.
Montri Maleewong, Roger H. J. Grimshaw
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Variational Principles and Solitary Wave Solutions of Generalized Nonlinear Schrödinger Equation in the Ocean [PDF]
Journal of Applied and Computational Mechanics, 2021 Internal solitary waves are very common physical phenomena in the ocean, which play an important role in the transport of marine matter, momentum and energy.
Meng-Zhu Liu +4 more
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Noncommutative Reduction of Nonlinear Schrödinger Equation on Lie Groups
Universe, 2022 We propose a new approach that allows one to reduce nonlinear equations on Lie groups to equations with a fewer number of independent variables for finding particular solutions of the nonlinear equations.
Alexander Breev +2 more
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