【摘要】 借助计算机代数系统Mathematica ,利用双曲函数法找到了组合KdV方程 (CombinedKdVEquation)的精确孤立波解 ,包括钟型孤立波解和扭结型孤立波解 .在此基础上又对双曲函数法的思想进行了推广 ,从而获得了其更多的显式精确解 ,包括间断型激波解和指数函数型解 .这种方法也适用于求解其他非线性发展方程 (组 ) .更多还原

【Abstract】 With the aid of computer algebraic system “Mathematica” and by using the hyperbola function method,the exact and solitary wave solutions of the combined KdV equation are obtained,including the bell like and the kink solitary wave solutions.The thought based on the hyperbola function method is extended,and more explicit and exact solutions are successfully derived,including shock wave type solutions with break point and exponential function type solutions.This method can be used also to solve other nonlinear evolution equation(s).更多还原