Double Periodic Wave Solutions of the (2 + 1)-Dimensional Sawada-Kotera Equation

Abstract

Based on a general Riemann theta function and Hirota’s bilinear forms, we devise a straightforward way to explicitly construct double periodic wave solution of $(2+1)$-dimensional nonlinear partial differential equation. The resulting theory is applied to the $(2+1)$-dimensional Sawada-Kotera equation, thereby yielding its double periodic wave solutions. The relations between the periodic wave solutions and soliton solutions are rigorously established by a limiting procedure.