Periodic wave solutions of the Boussinesq equation

The Boussinesq equation usually arises in a physical problem as a long wave equation. The present work extends the search of periodic wave solutions for it. The Hirota bilinear method and Riemann theta function are employed in the process. We also analyse the asymptotic property of periodic waves in detail. Furthermore, it is of interest to note that well-known soliton solutions can be reduced from the periodic wave solutions.