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

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.