Lie group analysis for short pulse equation

TL;DR

This paper applies Lie symmetry analysis to a general short pulse equation, extending previous work by Liu and Li, and identifies new symmetries and algebraic structures relevant for understanding its solutions.

Contribution

It introduces a generalized Lie symmetry framework for the short pulse equation, including optimal subalgebra systems and additional local symmetries, advancing the mathematical analysis of this equation.

Findings

Identified point, contact, and local symmetries of the equation.

Generalized previous results by Liu and Li.

Derived optimal system of Lie symmetry subalgebras.

Abstract

In this paper, the classical Lie symmetry analysis and the generalized form of Lie symmetry method are performed for a general short pulse equation. The point, contact and local symmetries for this equation are given. In this paper, we generalize the results of H. Liu and J. Li [1], and add some further facts, such as optimal system of Lie symmetry subalgebras and two local symmetries.