Nonlocal symmetry and exact solutions of the (2+1)-dimensional Gardner equation

Abstract

For the (2+1)-dimensional Gardner equation, the truncated Painlevé method is developed to obtain the nonlocal residual symmetry and Bäcklund transformation. And, the symmetry group transformation can be computed from the extended system. Moreover, (2+1)-dimensional Gardner equation is proved to be consistent Riccati expansion (CRE) solvable. With the help of the Riccati equation and the CRE method, we obtain the soliton–cnoidal wave interaction solution of the equation.