Explicit traveling wave solutions to nonlinear evolution equations

被引：1
作者：
Zhang, Linghai [1 ]
机构：
[1] Lehigh Univ, Dept Math, Bethlehem, PA 18015 USA
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2011年 / 32卷 / 06期
关键词：
Explicit traveling wave solutions; Nonlinear partial differential equations; Reduction of order; DE-VRIES EQUATION; DEVRIES-BURGERS EQUATION; (2+1)-DIMENSIONAL BOUSSINESQ EQUATION; GENERALIZED FISHER EQUATION; GINZBURG-LANDAU EQUATION; KLEIN-GORDON EQUATIONS; SOLITARY WAVES; KP EQUATION;
D O I：
10.1007/s11401-011-0674-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
First of all, some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations, nonlinear dissipative dispersive wave equations, nonlinear convection equations, nonlinear reaction diffusion equations and nonlinear hyperbolic equations, respectively.
引用
收藏
页码：929 / 964
页数：36
相关论文
共 45 条
[1]  
[Anonymous], MATH PRACTICE THEORY
[2]   TABLE OF SOLUTIONS OF ONE-DIMENSIONAL BURGERS EQUATION [J].
BENTON, ER ;
PLATZMAN, GW .
QUARTERLY OF APPLIED MATHEMATICS, 1972, 30 (02) :195-&
[3]   SHOCK-WAVES IN THE MODIFIED KORTEWEG-DE VRIES-BURGERS EQUATION [J].
BIKBAEV, RF .
JOURNAL OF NONLINEAR SCIENCE, 1995, 5 (01) :1-10
[4]   TRAVELING-WAVE SOLUTIONS TO THE KORTEWEG-DEVRIES-BURGERS EQUATION [J].
BONA, JL ;
SCHONBEK, ME .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1985, 101 :207-226
[5]   Soliton Solutions of the KP Equation and Application to Shallow Water Waves [J].
Chakravarty, S. ;
Kodama, Y. .
STUDIES IN APPLIED MATHEMATICS, 2009, 123 (01) :83-151
[6]   SOLITARY-WAVE SOLUTIONS TO BOUSSINESQ SYSTEMS WITH LARGE SURFACE TENSION [J].
Chen, Min ;
Nguyen, Nghiem V. ;
Sun, Shu-Ming .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 26 (04) :1153-1184
[7]   New explicit solitary wave solutions for (2+1)-dimensional Boussinesq equation and (3+1)-dimensional KP equation [J].
Chen, Y ;
Yan, ZY ;
Zhang, H .
PHYSICS LETTERS A, 2003, 307 (2-3) :107-113
[8]   Periodic and quasi-periodic solutions for the complex Ginzburg-Landau equation [J].
Chung, K. W. ;
Yuan, Xiaoping .
NONLINEARITY, 2008, 21 (03) :435-451
[9]   On solitary wave solutions of the compound Burgers-Korteweg-de Vries equation [J].
David, Claire ;
Fernando, Rasika ;
Feng, Zhaosheng .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2007, 375 (01) :44-50
[10]   Burgers-Korteweg-de Vries equation and its traveling solitary waves [J].
Feng, Zhao-sheng ;
Meng, Qing-guo .
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2007, 50 (03) :412-422
12345