Dynamical behaviours and exact travelling wave solutions of modified generalized Vakhnenko equation

被引：2

作者：

Xiao, Junjun ^{[1
]}

Feng, Dahe ^{[1
,2
]}

Meng, Xia ^{[1
]}

Cheng, Yuanquan ^{[1
]}

机构：

[1] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541004, Guangxi, Peoples R China

[2] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Guizhou, Peoples R China

来源：

PRAMANA-JOURNAL OF PHYSICS | 2017年 / 88卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Modified generalized Vakhnenko equation; cusped solitons; loop solitons; periodic cusp wave solutions; smooth periodic wave solutions; pseudopeakon solitons; smooth soliton solutions; SOLITON SOLUTION; EVOLUTION;

D O I：

10.1007/s12043-016-1321-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.

引用

页数：9

共 50 条

[31] Exact Travelling Wave Solutions of Richards' Equation by Modified F-expansion Method
Patel, Priyanka M.
Pradhan, Vikas H.
INTERNATIONAL CONFERENCE ON COMPUTATIONAL HEAT AND MASS TRANSFER (ICCHMT) - 2015, 2015, 127 : 759 - 766
[32] Group analysis of the modified generalized Vakhnenko equation
Hashemi, M. S.
Nucci, M. C.
Abbasbandy, S.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2013, 18 (04) : 867 - 877
[33] Travelling wave solutions to the generalized stochastic KdV equation
Wei, Cai-Min
Wang, Jian-Jun
CHAOS SOLITONS & FRACTALS, 2008, 37 (03) : 733 - 740
[34] Travelling wave solutions for a generalized double dispersion equation
Bruzon, M. S.
Gandarias, M. L.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (12) : E2109 - E2117
[35] Travelling wave solutions for a class of generalized KdV equation
Tang, Shengqiang
Zheng, Jianxian
Huang, Wentao
APPLIED MATHEMATICS AND COMPUTATION, 2009, 215 (07) : 2768 - 2774
[36] Elliptic Travelling Wave Solutions to a Generalized Boussinesq Equation
El Achab, Abdelfattah
ABSTRACT AND APPLIED ANALYSIS, 2014,
[37] Bounded travelling wave solutions for a modified form of generalized Degasperis-Procesi equation
He Bin
Rui Weiguo
Li Shaolin
Chen Chan
APPLIED MATHEMATICS AND COMPUTATION, 2008, 206 (01) : 113 - 123
[38] New exact travelling wave solutions of the generalized Zakharov equations
Zhang, Huiqun
REPORTS ON MATHEMATICAL PHYSICS, 2007, 60 (01) : 97 - 106
[39] Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
HUANG Ding-Jiang ZHANG Hong-Qing Department of Applied Mathematics
CommunicationsinTheoreticalPhysics, 2004, 42 (08) : 171 - 174
[40] Exact travelling wave solutions to a coupled nonlinear evolution equation
Huang, DJ
Zhang, HQ
COMMUNICATIONS IN THEORETICAL PHYSICS, 2004, 42 (02) : 171 - 174

← 1 2 3 4 5 →