[formula omitted]-soliton solutions and associated integrability for a novel (2+1)-dimensional generalized KdV equation.

In this paper, we investigate the integrability of a (2+1)-dimensional generalized KdV equation. In virtue of the Weiss–Tabor–Carnevale method and Kruskal ansatz, this equation can pass the Painlevé test. The truncated Painlevé expansion leads to the Bäcklund transformation and rational solutions. The bilinear Bäcklund transformation and Bell-polynomial-typed Bäcklund transformation are constructed with the Hirota bilinear method and Bell polynomials. It is proved that the (2+1)-dimensional generalized KdV equation can be regarded as an integrable model in sense of infinite conservation laws. The formula of N -soliton solutions is given and verified with the Hirota condition. The study of integrability provides theoretical guidance for solving equations and gives the possibility of the existence of exact solutions. • A novel (2+1)-dimensional generalized KdV equation is investigated, which can pass the Painlevé test and leads to the Bäcklund transformation with rational solutions. • The bilinear Bäcklund transformation and Bell-polynomial-typed Bäcklund transformation are constructed, which yield the Lax pair and the infinite conservation laws. • The formula of N -soliton solutions is given and verified with the Hirota condition. [ABSTRACT FROM AUTHOR]