Auto-Bäcklund transformation and new exact solutions of the generalized variable-coefficients two-dimensional Korteweg–de Vries model.

Describing plasma physics, cluster physics, and geophysical fluid dynamics, a generalized variable-coefficient two-dimensional Korteweg–de Vries (GVCKdV) model is hereby under investigation. In this paper, an extended-variable-coefficient homogeneous balance method with symbolic computation is used to obtain an auto-Bäcklund transformation, some rational solutions, and new soliton-type solutions for the GVCKdV model. The solutions of the well-known cylindrical Kadomtsev-Petviashvili equation can be recovered as special cases of the results obtained here. [ABSTRACT FROM AUTHOR]