用改进的代数方法构造(2+1)维ZK-MEW方程的精确行波解

韩众; 张玉峰; 赵忠龙

doi:10.3879/j.issn.1000-0887.2013.06.011

用改进的代数方法构造(2+1)维ZK-MEW方程的精确行波解

doi: 10.3879/j.issn.1000-0887.2013.06.011

中国矿业大学理学院,江苏徐州 221116

基金项目: 中央高校基本科研业务费专项资金资助项目(2013XK03；2012LWB51)

详细信息

作者简介:
韩众(1987—),男,安徽淮南人,硕士生(通讯作者.E-mail:zhangyfcumt@163.com)

中图分类号: O175.29
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- 文章访问数: 1498
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- 被引次数: 0
出版历程
- 收稿日期: 2012-10-09
- 修回日期: 2013-03-29
- 刊出日期: 2013-06-15

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

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

摘要

摘要: 利用一种改进的统一代数方法将构造(2+1)维ZKMEW((2+1)-dimensionalZakharov-Kuznetsovmodifiedequalwidth)方程精确行波解的问题转化为求解一组非线性的代数方程组．再借助于符号计算系统Mathematica求解所得到的非线性代数方程组,最终获得了方程的多种形式的精确行波解．其中包括有理解,三角函数解,双曲函数解,双周期Jacobi椭圆函数解,双周期Weierstrass椭圆形式解等．并给出了部分解的图形.
- 改进的代数方法 /
- (2+1)维ZK-MEW方程 /
- 精确行波解
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

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参考文献(10)

[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.