Travelling wave solutions and proper solutions to the two-dimensional Burgers-Korteweg-de Vries equation

被引：15
作者：
Feng, ZS [1 ]
机构：
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2003年 / 36卷 / 33期
关键词：
D O I：
10.1088/0305-4470/36/33/307
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we study the two-dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analysing an equivalent two-dimensional autonomous system, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded travelling wave solution. Then by using a direct method, a travelling solitary wave solution to the 2D-BKdV equation is expressed explicitly, which appears to be more efficient than the existing methods proposed in the literature. At the end of the paper, the asymptotic behaviour of the proper solutions of the 2D-BKdV equation is established by applying the qualitative theory of differential equations.
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页码：8817 / 8827
页数：11
相关论文
共 24 条
[1]  
Abramowitz M., 1964, HDB MATH FUNCTIONS F
[2]  
BARRERA P, 1986, NUOVO CIMENTO B, V92, P142, DOI 10.1007/BF02732643
[3]   Modified extended tanh-function method for solving nonlinear partial differential equations [J].
Elwakil, SA ;
El-labany, SK ;
Zahran, MA ;
Sabry, R .
PHYSICS LETTERS A, 2002, 299 (2-3) :179-188
[4]   Extended tanh-function method and its applications to nonlinear equations [J].
Fan, EG .
PHYSICS LETTERS A, 2000, 277 (4-5) :212-218
[5]   A new complex line soliton for the two-dimensional KdV-Burgers equation [J].
Fan, EG ;
Zhang, J ;
Hon, BYC .
PHYSICS LETTERS A, 2001, 291 (06) :376-380
[6]  
FENG Z, 1997, MATH PRAC THEORY, V27, P222
[7]   Exact solution in terms of elliptic functions for the Burgers-Korteweg-de Vries equation [J].
Feng, ZS .
WAVE MOTION, 2003, 38 (02) :109-115
[8]   The first integral method to the two-dimensional Burgers-Korteweg-de Vries equation [J].
Feng, ZS ;
Wang, XH .
PHYSICS LETTERS A, 2003, 308 (2-3) :173-178
[9]   Exact solution to an approximate sine-Gordon equation in (n+1)-dimensional space [J].
Feng, ZS .
PHYSICS LETTERS A, 2002, 302 (2-3) :64-76
[10]  
Feng ZS, 2002, DYNAM CONT DIS SER A, V9, P563
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