scholarly journals Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear Terms

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Heng Wang ◽  
Longwei Chen ◽  
Hongjiang Liu ◽  
Shuhua Zheng
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Travelling Wave ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Phase Portraits ◽  
Travelling Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

By using the method of dynamical system, the exact travelling wave solutions of the higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms are studied. Based on this method, all phase portraits of the system in the parametric space are given with the aid of the Maple software. All possible bounded travelling wave solutions, such as solitary wave solutions, kink and anti-kink wave solutions, and periodic travelling wave solutions, are obtained, respectively. The results presented in this paper improve the related previous conclusions.

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.

Bifurcation Behaviour of the Travelling Wave Solutions of the Perturbed Nonlinear Schrödinger Equation with Kerr Law Nonlinearity

2011 ◽  
Vol 66 (12) ◽  
pp. 721-727 ◽  
Author(s):  
Zai-Yun Zhang ◽  
Xiang-Yang Gan ◽  
De-Ming Yu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Travelling Wave ◽  
Nonlinear Schrodinger Equation ◽  
Travelling Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Kerr Law ◽  
Kerr Law Nonlinearity

In this paper, we study the bifurcations and dynamic behaviour of the travelling wave solutions of the perturbed nonlinear Schrödinger equation (NLSE) with Kerr law nonlinearity by using the theory of bifurcations of dynamic systems. Under the given parametric conditions, all possible representations of explicit exact solitary wave solutions and periodic wave solutions are obtained

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