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The simple direct method is adopted to find Non-Auto-Backlund transformation   for variable coefficient non-linear systems. The (2+1)-dimensional   generalized Kadomtsev-Petviashvili equation with variable coefficients is   used as an example to elucidate the solution procedure, and its symmetry   transformation and exact solutions are obtained

Lie symmetry and exact solution of (2+1)-dimensional generalized Kadomtsev-Petviashvili equation with variable coefficients