Exact solutions of some nonlinear partial differential equations using functional variable method

摘要

The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Kleina€“Gordon equation, the (2 + 1)-dimensional Camassaa€“Holm Kadomtseva€“Petviashvili equation and the higher-order nonlinear Schr??dinger equation. By using this useful method, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. It is shown that the proposed method is effective and general.