MBBM方程的一类精确解

利用齐次平衡法并借助一维立方非线性Klein-Gordon方程的精确解,将一个难于求解的非线性偏微分方程化为一个易于求解的代数方程组然后用待定系数法确定相应的常数,简洁地求得MBBM方程的精确解。这些解中包含三角函数解,Jacobi椭圆函数解等。同时这种方法还可以可应用于其他的非线性发展方程的求解.

A Class of Exact Solutions of the MBBM Equations

Using the homogeneous balance method and the accurate solution of one-dimensional cubic nonlinear Klein-Gordon equation as a class of nonlinear partial differential equations that are hard to be solved by the usual ways can be reduced to a set of easily solved algebraic equations,and their related coefficients can be easily determined by the undetermined coefficients method.Then,the exact analytical solutions of MBBM equation can be obtained.These solutions contain triangular periodic solutions,Jacobi elliptic function solutions and so on.The approach presented in the paper may be used to other nonlinear evolution equations for generating solutions.