Consistent KdV expansion method and its applications to the KP equation

Abstract

This paper proposed a novel method, named as the Consistent KdV equation Expansion (CKdVE) method, for solving nonlinear differential equations with the help of the classical nonlinear KdV equation. If a system satisfies the CKdVE, then it can be defined as CKdVE solvability. Especially, the Kadomtsev–Petviashvili (KP) equation is also verified as a typical case of the CKdVE solvability. Moreover, the detailed discussion illustrates the effectiveness and convenience of the proposed method, and presents the possibility of constructing relationships among many different partial differential equation models in the related field.