Bäcklund transformation, Lax pair, infinite conservation laws and exact solutions to a generalized (2 + 1)-dimensional equation

Abstract

In this paper, the integrability of a generalized ([Formula: see text])-dimensional equation is investigated by using the Bell polynomials and Hirota bilinear method. By appropriate transformation, the bilinear equation is constructed. Some soliton solutions are yielded via the Hirota bilinear method. Then the evolution and collision of the soliton solutions are discussed. Starting from the two-field condition, the bilinear Bäcklund transformation is derived. Linearization of the [Formula: see text]-polynomials-typed Bäcklund transformation leads to the Lax pair. Besides, infinite conservation laws are derived by constructing the Riccati-type equation and devergence-type equation.