On the (2+1)-dimensional Gardner equation: Determinant solutions and pfaffianization

In this paper, we first present the Casorati and Grammian determinant solutions to the (2+1)-dimensional Gardner equation. Then, by using the pfaffianization procedure of Hirota and Ohta, a new integrable coupled system is generated from the Gardner equation. Moreover, Gramm-type pfaffian solutions to the pfaffianized system are proposed.