Lie symmetry analysis and one-dimensional optimal system for the generalized 2+1 Kadomtsev-Petviashvili equation

Abstract

We classify the Lie point symmetries for the 2+1 nonlinear generalized Kadomtsev-Petviashvili equation by determine all the possible f(u) 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.

15 pages, 8 tables, no figures

References in corpus (1)

• Similarity Solutions For The Complex Burgers' Hierarchy

Cited by in corpus (2)

• Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations
• Exact Anti-Self-Dual four-manifolds with a Killing symmetry by similarity transformations