Wronskian solution, Bäcklund transformation and Painlevé analysis to a (2+1)-dimensional Konopelchenko-Dubrovsky equation

The main work of this paper is to construct the Wronskian solution and investigate the integrability characteristics of the (2 + 1)-dimensional Konopelchenko-Dubrovsky equation. Firstly, the Wronskian technique is used to acquire a sufficient condition of the Wronskian solution. According to the Wronskian form, the soliton solution is obtained by selecting the elements in the determinant that satisfy the linear partial differential systems. Secondly, the bilinear B & auml;cklund transformation and Bell-polynomial-typed B & auml;cklund transformation are derived directly via the Hirota bilinear method and the Bell polynomial theory, respectively. Finally, Painlev & eacute; analysis proves that this equation possesses the Painlev & eacute; property, and a Painlev & eacute;-typed B & auml;cklund transformation is constructed to solve a family of exact solutions by selecting appropriate seed solution. It shows that the Wronskian technique, B & auml;cklund transformation, Bell polynomial and Painlev & eacute; analysis are applicable to obtain the exact solutions of the nonlinear evolution equations, e.g., soliton solution, single-wave solution and two-wave solution.