mKdV方程的一类新的精确孤立波解  

A class of new exact solitary wave solutions of the mKdV equation

作　　者：李晓燕[1] 张英[1] 姚若侠[1] 

机构地区：[1]陕西师范大学计算机科学学院,陕西西安710062

出　　处：《宝鸡文理学院学报（自然科学版）》2013年第2期1-4,8,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11071278;11172342);中央高校基本科研业务费专项资金项目(GK201302026)

摘　　要：目的以mKdV方程为例,研究非线性偏微分方程精确孤立波解的求解新方法。方法通过引入新的行波变换ξ=κv+t,v=v(x,t),主要利用改进的Tanh函数展开方法与齐次平衡法。结果与结论获得mKdV方程形式更为丰富的新的精确孤立波解,并证明了改进的Tanh函数法在求解非线性发展方程新的精确解方面的有效性。该方法也适用于其它的非线性发展方程(组)。Objective-To study new method of exact solitary wave solutions for solving nonlinear partial differential equations. Methods-By introducing a new traveling wave transformation ξ=κv＋t,v=v（x,t）, the modified hyperbolic tangent function method and homogeneous balance method are mainly used. Results and Conclusion-More plentiful forms of new exact solitary wave solutions of the mKdV equation are obtained and the effectiveness of the modified hyperbolic tangent function method in obtaining new exact solutions of nonlinear evolution equations is demonstrated. The proposed new method can be applied to other nonlinear evolution equations.

关 键 词：改进的Tanh函数法 MKDV方程 齐次平衡法 符号计算 精确孤立波解 

分 类 号：O175[理学—数学]