Lie symmetry analysis and one-dimensional optimal system for the generalized 2 + 1 Kadomtsev-Petviashvili equation
Andronikos Paliathanasis
Abstract
Abstract We classify the Lie point symmetries for the 2 + 1 nonlinear generalized Kadomtsev-Petviashvili equation by determine all the possible <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>f</mml:mi> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> 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.