Results 1 to 10 of about 2,459 (109)

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
doaj   +2 more sources

Impact of Brownian motion on the optical soliton solutions for the three component nonlinear Schrödinger equation [PDF]

Scientific Reports
In 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, Tahir Shahzad, Wael W. Mohammed, Nauman Ahmed, Baboucarr Ceesay, Muhammad Waqas Yasin   +5 more
doaj   +2 more sources

RETRACTED ARTICLE: Propagation of wave insights to the Chiral Schrödinger equation along with bifurcation analysis and diverse optical soliton solutions

Scientific Reports
In 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
doaj   +2 more sources

Discrete and Semi-Discrete Multidimensional Solitons and Vortices: Established Results and Novel Findings [PDF]

Entropy
This 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
doaj   +2 more sources

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
doaj   +1 more source

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
doaj   +1 more source

Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients

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
doaj   +1 more source

N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics, 2021
In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given.
Yu-Shan Bai, Peng-Xiang Su, Wen-Xiu Ma
doaj   +1 more source

A Study of Traveling Wave Structures and Numerical Investigations into the Coupled Nonlinear Schrödinger Equation Using Advanced Mathematical Techniques

Mathematics, 2023
This article explores adapted mathematical methods to solve the coupled nonlinear Schrödinger (C-NLS) equation through analytical and numerical methods.
Taghread Ghannam Alharbi, Abdulghani Alharbi   +1 more
doaj   +1 more source

Pöppe triple systems and integrable equations

Partial Differential Equations in Applied Mathematics, 2023
We construct the combinatorial Pöppe triple system, or ternary algebra, that underlies the non-commutative nonlinear Schrödinger (NLS) and modified Korteweg–de Vries (mKdV) hierarchy.
Anastasia Doikou, Simon J.A. Malham, Ioannis Stylianidis, Anke Wiese   +3 more
doaj   +1 more source