Bifurcation and new exact traveling wave solutions to time-space coupled fractional nonlinear Schrödinger equation

2021 ◽  
Vol 395 ◽  
pp. 127217
Author(s):  
Tianyong Han ◽  
Zhao Li ◽  
Xue Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Traveling Wave ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Time Space ◽  
Fractional Nonlinear Schrödinger Equation

Exact traveling wave solutions to the nonlinear Schrödinger equation

2014 ◽  
Vol 233 ◽  
pp. 109-115 ◽  
Author(s):  
Saïdou Abdoulkary ◽  
Alidou Mohamadou ◽  
Tibi Beda ◽  
Betchewe Gambo ◽  
Serge Y. Doka ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Traveling Wave ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Exact Traveling Wave Solutions ◽  
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.

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