Symmetry Analysis for a Generalized Kadomtsev-Petviashvili Equation

Abstract

A generalized Kadomtsev-Petviashvili equation (GKPE) $(u_t+u u_x + \beta(t)u +\gamma(t)u_{xxx})_x+\sigma(t)u_{yy}\ = \ 0$ 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.