Symmetries, conservation laws, and line soliton solutions of a two-dimensional generalized kdv equation with p-POWER

Abstract

ct. A two-dimensional generalization of the Korteweg-de Vries (KdV) equation with p-power was studied. This equation appeared in many physical applications. For p > 0, we derived all point symmetries and conservation laws including those existing for special powers. The conserved quantities were studied. We also determined an explicit line soliton solution using some invariant under translation conservation laws for p > 0. Finally, by using invariant under scaling conservation laws, we reduced the traveling wave ordinary differential equation for different values o p.