Exact Travelling Wave Solutions for the (2+1)-Dimensional ZK-MEW Equation by Using an Improved Algebra Method

HAN Zhong; ZHANG Yu-feng; ZHAO Zhong-long

doi:10.3879/j.issn.1000-0887.2013.06.011

Volume 34 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2013 > 34(6): 651-660

HAN Zhong, ZHANG Yu-feng, ZHAO Zhong-long. Exact Travelling Wave Solutions for the (2+1)-Dimensional ZK-MEW Equation by Using an Improved Algebra Method[J]. Applied Mathematics and Mechanics, 2013, 34(6): 651-660. doi: 10.3879/j.issn.1000-0887.2013.06.011

Citation:

PDF( 1907 KB)

Exact Travelling Wave Solutions for the (2+1)-Dimensional ZK-MEW Equation by Using an Improved Algebra Method

doi: 10.3879/j.issn.1000-0887.2013.06.011

School of Sciences, China University of Mining and Technology,Xuzhou, Jiangsu 221116, P.R.China

Received Date: 2012-10-09
Rev Recd Date: 2013-03-29
Publish Date: 2013-06-15

Abstract

Abstract

Based upon an improved unified algebra method and implement in the symbolic computation system Mathematica, the (2+1)-dimensional ZakharovKuznetsov modified equal width equation was considered. This method converted the work of constructing exact travelling wave solutions for an equation into solving a system of nonlinear algebra equations(NLAEs). After solving the system of nonlinear algebra equations, abundant general form solutions are obtained, which including rational function solutions, trigonometric function solutions, hyperbolic function solutions, Jacobi elliptic function solutions, Weierstrass elliptic function solutions. The profiles of some obtained solutions are also given out.
- improved algebra method,
- (2+1)-dimensional ZK-MEW equation,
- exact travelling wave solutions

FullText(HTML)

References(10)

References

[1]	Fan E G. Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method[J]. Journal of Physics A: Mathematical and General,2002, 35(32): 6853-6872.
[2]	Yan Z Y. An improved algebraic method and it applications in nonlinear wave equations[J]. Chaos, Solitons & Fractals,2004, 21(4): 1013-1021.
[3]	曾昕, 张鸿庆. (2+1)维色散长波方程的新的类孤子解[J]. 物理学报, 2005, 54(2): 504-510. (ZENG Xin, ZHANG Hong-qing. New solitonlike solutions to the (2+1)-dimensional dispersive long wave equations[J].Acta Physica Sinica, 2005, 54(2): 504-510.(in Chinese))
[4]	长勒, 斯仁道尔吉. 变系数组合KdV方程的精确类孤子解[J]. 内蒙古师范大学学报(自然科学汉文版), 2011, 40(6): 552-555. (Changle, Sirendaoerji. Exact soliton-like solutions of the variable coefficient compound KdV equation[J]. Journal of Inner Mongolia Normal University (Natural Science Edition), 2011, 40(6): 552-555.(in Chinese))
[5]	套格图桑, 斯仁道尔吉. 构造变系数非线性发展方程精确解的一种方法[J]. 物理学报, 2009, 58(4): 2121-2126. (Taogetusang, Sirendaoerji. A method for constructing exact solutions of nonlinear evolution equation with variable coefficients[J]. Acta Physica Sinica, 2009, 58(4): 2121-2126.(in Chinese))
[6]	Sirendaoerji. A new application of the extended tanhfunction method[J]. 内蒙古师范大学学报（自然科学汉文版）， 2007, 36(4): 393-401.(Sirendaoerji. A new application of the extended tanh-function method[J]. Journal of Inner Mongolia Normal University (Natural Science Edition),2007, 36(4): 393-401.)
[7]	Khalique C M, Adem K R. Exact solutions of the (2+1)-dimensional Zakharov-Kuznetsov modified equal width equation using Lie group analysis[J]. Mathematical and Computer Modelling,2011, 54(1/2): 184-189.
[8]	Wazwaz A M. Exact solutions for the ZK-MEW equation by using the tanh and sinecosine methods[J]. International Journal of Computer Mathematics,2005, 82(6): 699-708.
[9]	Wazwaz A M. The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants[J]. Communications in Nonlinear Science and Numerical Simulation, 2006, 11(2): 148-160.
[10]	Tascan F, Bekir A, Koparan M. Traveling wave solution of nonlinear evolution equations by using the first integral methods[J]. Communications in Nonlinear Science and Numerical Simulation,2009, 14(5): 1810-1815.