Further improved F-expansion method and new exact solutions of Kadomstev–Petviashvili equation

In this paper, the generalized F-expansion method [Chen J, He HS, Yang KQ. Commun Theor Phys (Beijing, China) 2005;44:307] is improved and a further improved F-expansion method is proposed to seek more types of exact solutions of non-linear evolution equations. With the aid of symbolic computation, we choose the (3 + 1)-dimensional Kadomstev–Petviashvili equation to illustrate the validity and advantages of the proposed method. As a result, many new and more general solutions are obtained including single and combined non-degenerate Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions. This method can also be applied to other non-linear evolution equations in mathematical physics.