Double periodic wave solutions of the \((2 + 1)\)-dimensional Sawada-Kotera equation (Q1724336)

Summary: 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.