Exact traveling wave solutions and bifurcations of the generalized derivative nonlinear Schrödinger equation

2016 ◽  
Vol 85 (2) ◽  
pp. 1031-1037 ◽  
Author(s):  
Temesgen Desta Leta ◽  
Jibin Li
2021 ◽  
Author(s):  
Lu Tang ◽  
Shanpeng Chen

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.


2012 ◽  
Vol 22 (05) ◽  
pp. 1250121 ◽  
Author(s):  
FANG YAN ◽  
HAIHONG LIU

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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