ANALYTIC ANALYSIS ON A GENERALIZED (2+1)-DIMENSIONAL VARIABLE-COEFFICIENT KORTEWEG–DE VRIES EQUATION USING SYMBOLIC COMPUTATION

With the help of symbolic computation, a generalized (2+1)-dimensional variable-coefficient Korteweg–de Vries equation is studied for its Painlevé integrability. Then, Hirota bilinear form is derived, from which the one- and two-solitary-wave solutions with the corresponding graphic illustration are presented. Furthermore, a bilinear auto-Bäcklund transformation is constructed and the nonlinear superposition formula and Lax pair are also obtained. Finally, the analytic solution in the Wronskian form is constructed and proved by direct substitution into the bilinear equation.