Solitons and (semi-)rational solutions for the (2+1)-dimensional Gardner equation

In this letter, we study the (2+1)-dimensional Gardner equation based on the Hirota’s bilinear method and the reduction of the KP hierarchy. Starting from the Grammian determinant solution, we first give two-soliton solutions on the constant and periodic background, respectively. Furthermore, we construct fundamental rational solution, multiple rational solution and semi-rational solution by applying differential operators to parameters. Dynamics of (semi-)rational solutions are analyzed with plots.