N-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 Painleve test. The truncated Painleve expansion leads to the Backlund transformation and rational solutions. The bilinear Backlund transformation and Bell-polynomial-typed Backlund 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.

Automated summary

In this paper, the integrability of a (2+1)-dimensional generalized KdV equation is investigated. The equation passes the Painleve test by using the Weiss-Tabor-Carnevale method and Kruskal ansatz. The truncated Painleve expansion leads to the Backlund transformation and rational solutions. The bilinear Backlund transformation and Bell-polynomial-typed Backlund transformation are constructed using the Hirota bilinear method and Bell polynomials. It is proven that the (2+1)-dimensional generalized KdV equation can be regarded as an integrable model in terms 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 suggests the existence of exact solutions.