Abstract
In this paper, the modified CK's direct method to findsymmetry groups of nonlinear partial differential equation is extended to(2+1)-dimensional variable coefficient canonical generalized KP (VCCGKP)equation. As a result, symmetry groups, Lie point symmetry group and Liesymmetry for the VCCGKP equation are obtained. In fact, the Lie pointsymmetry group coincides with that obtained by the standard Lie groupapproach. Applying the given Lie symmetry, we obtain five types ofsimilarity reductions and a lot of new exact solutions,including hyperbolic function solutions, triangular periodicsolutions, Jacobi elliptic functionsolutions and rational solutions, for the VCCGKP equation.
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