Conservation laws, symmetries, and line solitons of a Kawahara-KP equation

Abstract

A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries are obtained and used to derive conservation laws via Noether’s theorem by introduction of a potential which gives a Lagrangian formulation for the equation. The meaning and properties of the symmetries and the conserved quantities are described. Explicit sech-type line wave solutions are found and their features are discussed. They are shown to describe dark solitary waves on a background which depends on a dispersion ratio and on the speed and direction of the waves. The zero-background case is explored.