Abstract
We classify the Lie point symmetries for the 2 + 1 nonlinear generalized Kadomtsev-Petviashvili equation by determine all the possible functional forms where the latter depends. For each case the one-dimensional optimal system is derived; a necessary analysis to find all the possible similarity transformations which simplify the equation. We demonstrate our results by constructing static and travel-wave similarity solutions. In particular the latter solutions satisfy a second-order nonlinear ordinary differential equation which can be solved by quadratures.
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