Bilinear B(A|¨)cklund Transformation And Lax Pairs For KdV Equation Set And Boussinesq Equation Set

Nonlinear partial diferential equation is a kind of mathematical tools to describenatural phenomena. Finding the solutions of nonlinear partial diferential equations isvery important and forefront research topics. Hirota method is produced under thisbackground, Hirota method is mainly by transforming the nonlinear equations into linearequations, then using perturbation method to solve. In the research of partial diferentialequations, Lax pairs and B(a|¨)cklund transformation are very important.Similar to partialdiferential equations,we can can also use the appropriate method to obtain the bilinearB(a|¨)cklund transformation. We can produce Lax pair, a new soliton equations, and Miuratransformation with B(a|¨)cklund transformation.In this article, we mainly study of KdV equation set and Boussinesq equation set.Throughappropriate elimination method,the new bilinear equations would be obtained. In or-der to discuss nonlinear partial diferential equations which correspond to the bilinearequations,we frst obtain bilinear B(a|¨)cklund transformation for the two sets of equa-tions.Starting from these bilinear B(a|¨)cklund transformations,Lax pairs for KdV equationset and Boussinesq equation set are derived. Because the Lax pairs satisfy the zero cur-vature equation,that means the new system of equations are Lax integrable.