Improved tanh-function method and the new exact solutions for the general variable coefficient KdV equation and MKdV equation

In this paper, by using the extended tanh-function method, the general variable coefficient KdV and MKdV equations are reduced to first-order variable coefficient nonlinear ordinary differential equations, and then the new exact solutions for these equations, which include exact soliton-like, rational formal and triangle function solutions, are obtained through solving these ordinary differential equations.