Solitons, Bäcklund transformation, and Lax pair for the (2+1)-dimensional Boiti–Leon–Pempinelli equation for the water waves

Abstract

Under investigation in this paper is the (2+1)-dimensional Boiti–Leon–Pempinelli (BLP) equation for the water waves. By virtue of the binary Bell polynomials and symbolic computation, the bilinear form for the BLP equation is obtained. Furthermore, soliton solutions are presented, and soliton interaction properties including the elastic, inelastic, and elastic-inelastic collisions are discussed by the graphical analysis. Besides, the Bäcklund transformation in the form of the binary Bell polynomials is derived. Via the Bäcklund transformation, the shock-wave solutions and Lax pair are both constructed.