On exact solutions of some higher-dimensional nonlinear partial differential equations

Abstract

In this paper, new explicit and exact travelling wave solutions for some nonlinear partial differential equations are obtained by using the hyperbolic function method and the Jacobi elliptic function method, in which these equations are (2+1)-dimensional generalization of the Korteweg and de Vries equation, (2+1)-dimensional Boussinesq equation and (3+1)-dimensional Kadomtsev–Petviashvili equation. In addition, the properties of these equations are shown with figures.