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arXiv · 1003.2513

Symmetry Analysis for a Generalized Kadomtsev-Petviashvili Equation

B. Mayil Vaganan·D. Pandiaraja·M. Senthilkumaran
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Abstract

A generalized Kadomtsev-Petviashvili equation (GKPE) $(u_t+u u_x + β(t)u +γ(t)u_{xxx})_x+σ(t)u_{yy}\ = \ 0$ is shown to admit an infinite-dimensional Lie group of symmetries when $\bt(t), \ga(t)$ and $\si(t)$ are arbitrary. The Lie algebra of this symmetry group contains two arbitrary functions $f(t)$ and $g(t)$. Further, low-dimensional subalgebras and physically meaningful five dimensional Lie algebra containing translation and Galilei transformation are derived. A solution of GKPE involving two arbitrary functions of time $t$, in addition to $f(t)$ and $g(t)$, is obtained using an one-dimensional subalgebra.

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B. Mayil Vaganan, D. Pandiaraja, M. Senthilkumaran. 2010-03-12. Symmetry Analysis for a Generalized Kadomtsev-Petviashvili Equation. https://arxiv.org/abs/1003.2513

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