Explicit and exact solutions of the combined KdV equation

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).