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

TL;DR

This paper investigates a generalized Kawahara-KP equation, deriving symmetries, conservation laws, and explicit line soliton solutions, revealing their physical properties and dependence on dispersion and wave parameters.

Contribution

It introduces a new higher-order dispersive KP equation, derives its symmetries and conservation laws, and constructs explicit line soliton solutions with physical interpretations.

Findings

Derived Lie point symmetries and conservation laws.

Found explicit line soliton solutions describing dark solitary waves.

Analyzed the influence of dispersion ratio and wave parameters on solutions.

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 line soliton 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.