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

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

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 so...

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Main Authors: Heng Wang, Longwei Chen, Hongjiang Liu, Shuhua Zheng
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2016/7405141
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spelling doaj-fa3f3633d77b4cbc9989d5d8b27d2c0c2020-11-24T22:07:44ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472016-01-01201610.1155/2016/74051417405141Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear TermsHeng Wang0Longwei Chen1Hongjiang Liu2Shuhua Zheng3College of Statistics and Mathematics, Yunnan University of Finance and Economics Kunming, Yunnan 650221, ChinaCollege of Statistics and Mathematics, Yunnan University of Finance and Economics Kunming, Yunnan 650221, ChinaCity and Environment College, Yunnan University of Finance and Economics Kunming, Yunnan 650221, ChinaCollege of Statistics and Mathematics, Yunnan University of Finance and Economics Kunming, Yunnan 650221, ChinaBy 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.http://dx.doi.org/10.1155/2016/7405141
collection DOAJ
language English
format Article
sources DOAJ
author Heng Wang
Longwei Chen
Hongjiang Liu
Shuhua Zheng
spellingShingle Heng Wang
Longwei Chen
Hongjiang Liu
Shuhua Zheng
Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear Terms
Mathematical Problems in Engineering
author_facet Heng Wang
Longwei Chen
Hongjiang Liu
Shuhua Zheng
author_sort Heng Wang
title Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear Terms
title_short Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear Terms
title_full Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear Terms
title_fullStr Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear Terms
title_full_unstemmed Nonlinear Dynamics and Exact Traveling Wave Solutions of the Higher-Order Nonlinear Schrödinger Equation with Derivative Non-Kerr Nonlinear Terms
title_sort nonlinear dynamics and exact traveling wave solutions of the higher-order nonlinear schrödinger equation with derivative non-kerr nonlinear terms
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2016-01-01
description 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.
url http://dx.doi.org/10.1155/2016/7405141
work_keys_str_mv AT hengwang nonlineardynamicsandexacttravelingwavesolutionsofthehigherordernonlinearschrodingerequationwithderivativenonkerrnonlinearterms
AT longweichen nonlineardynamicsandexacttravelingwavesolutionsofthehigherordernonlinearschrodingerequationwithderivativenonkerrnonlinearterms
AT hongjiangliu nonlineardynamicsandexacttravelingwavesolutionsofthehigherordernonlinearschrodingerequationwithderivativenonkerrnonlinearterms
AT shuhuazheng nonlineardynamicsandexacttravelingwavesolutionsofthehigherordernonlinearschrodingerequationwithderivativenonkerrnonlinearterms
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