By using the WTC method and symbolic computation, we apply the Painlevé test for a (2+1)-dimensional variable-coefficient Kortweg-de Vries (KdV) equation, and the considered equation is found to possess the Painlevé property without any parametric constraints. The auto-Bǎcklund transformation and several types of exact solutions are obtained by using the Painlevé truncated expansion method. Finally, the Hirota’s bilinear form is presented and multi-soliton solutions are also constructed.
Yu, Zhang and Gui-Qiong, Xu
Integrability and Exact Solutions for a (2+1)-dimensional Variable-Coefficient KdV Equation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 9,
2, Article 13.
Available at: https://digitalcommons.pvamu.edu/aam/vol9/iss2/13