New soliton-like and periodic-like solutions for the KdV equation

In this paper based on a system of Riccati equations, a newly generally projective Riccati equation expansion method is presented. It is direct and more powerful than the tanh-function method, generally projective Riccati equation method and can be used to construct more new exact solutions of nonlinear differential equations in mathematical physics. The well-known KdV equation is chosen to illustrate the algorithm such that more families of new explicit solutions are obtained, which contain soliton-like and periodic-like solutions. This algorithm can also be applied to many other nonlinear differential equations.