Binary Bell Polynomials, Bilinear Approach to Exact Periodic Wave Solutions of (2 + 1)-Dimensional Nonlinear Evolution Equations

Abstract

In the present letter, we get the appropriate bilinear forms of (2 + 1)-dimensional KdV equation, extended (2 + 1)-dimensional shallow water wave equation and (2 + 1)-dimensional Sawada—Kotera equation in a quick and natural manner, namely by appling the binary Bell polynomials. Then the Hirota direct method and Riemann theta function are combined to construct the periodic wave solutions of the three types nonlinear evolution equations. And the corresponding figures of the periodic wave solutions are given. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.