New solutions of the general elliptic equation and its applications to the new (3 + 1)-dimensional integrable Kadomtsev-Petviashvili equation

Abstract

Abstract In this article, we introduce many new Jacobi elliptic function solutions to the general elliptic equation. Consequently, the Jacobi elliptic function expansion method is improved to accommodate the general elliptic equation and its new solutions for constructing exact traveling wave solutions of nonlinear partial differential equations (NLPDEs). Moreover, the improved method is used to obtain new explicit solutions for the (3+1)-dimensional integrable Kadomtsev-Petviashvili (KP) equation. This method can be applied to many other NLPDEs as well for obtaining new exact solutions.