Bilinear B\"acklund transformations and Lax pair for the Boussinesq equation

Hirota’s bilinear approach is a very effective method to construct solutions for soliton systems. In terms of this method, the nonlinear equations can be transformed into linear equations, and can be solved by using perturbation method. In this paper, we study the bilinear Boussinesq equation and obtain its bilinear B"{a}cklund transformation. Starting from this bilinear B"{a}cklund transformation, we also derive its Lax pair and test its integrability.