scholarly journals The classification of single traveling wave solutions for the fractional coupled nonlinear Schrödinger equation

2022 ◽  
Vol 54 (2) ◽  
Author(s):  
Lu Tang ◽  
Shanpeng Chen
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Traveling Wave ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Wave Solutions

scholarly journals The Classification of Single Traveling Wave Solutions for the Fractional Coupled Nonlinear SchrÖdinger equation

2021 ◽  
Author(s):  
Lu Tang ◽  
Shanpeng Chen
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Traveling Wave ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Hyperbolic Function ◽  
Nonlinear Schrödinger ◽  
Coupled Nonlinear Schrödinger Equation ◽  
Wave Solutions

Abstract The main purpose of this paper is to study the single traveling wave solutions of the fractional coupled nonlinear SchrÖdinger equation. By using the complete discriminant system method and computer algebra with symbolic computation, a series of new single traveling wave solutions are obtained, which include trigonometric function solutions, Jacobi elliptic function solutions, hyperbolic function solutions, solitary wave solutions and rational function solutions. In order to further explain the propagation of the fractional coupled nonlinear Schr\"{o}dinger equation in nonlinear optics, two-dimensional and three-dimensional graphs are drawn.

BIFURCATION OF PHASE AND EXACT TRAVELING WAVE SOLUTIONS OF A HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION

2012 ◽  
Vol 22 (05) ◽  
pp. 1250121 ◽  
Author(s):  
FANG YAN ◽  
HAIHONG LIU
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Traveling Wave ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Phase Portraits ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

The dynamical behavior of a higher-order nonlinear Schrödinger equation is studied by using the bifurcation theory method of dynamical systems. With the aid of Maple, all bifurcations and phase portraits in the parametric space are obtained. Moreover, some new traveling wave solutions corresponding to the orbits on phase portraits are given, which include solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions.

scholarly journals Bifurcation Analysis and Solutions of a Higher-Order Nonlinear Schrödinger Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Yi Li ◽  
Wen-rui Shan ◽  
Tianping Shuai ◽  
Ke Rao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Traveling Wave ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Phase Portraits ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

The purpose of this paper is to investigate a higher-order nonlinear Schrödinger equation with non-Kerr term by using the bifurcation theory method of dynamical systems and to provide its bounded traveling wave solutions. Applying the theory, we discuss the bifurcation of phase portraits and investigate the relation between the bounded orbit of the traveling wave system and the energy level. Through the research, new traveling wave solutions are given, which include solitary wave solutions, kink wave solutions, and periodic wave solutions.

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