Bäcklund transformation classification, integrability and exact solutions to the generalized Burgers’–KdV equation

This paper is concerned with the Bäcklund transformations (BTs) of the nonlinear evolution equations (NLEEs). Based on the homogeneous balance principle (HBP), the existence of the BT of the generalized Burgers’–KdV (B–KdV) equation is classified, then the BTs of the nonlinear equations are given. In general, the method can be used to construct BTs of the nonlinear evolution equations in polynomial form. Furthermore, the integrability and exact explicit solutions to the nonlinear equations are investigated.