Symmetry group theorem to the Lin-Tsien equation and conservation laws relating to the symmetry of the equation?

TL;DR

This paper derives the symmetry group theorem for the Lin-Tsien equation using a modified direct method and uncovers associated conservation laws linked to its symmetry algebra.

Contribution

It introduces a novel application of the modified CK's direct method to derive symmetry groups and conservation laws for the Lin-Tsien equation.

Findings

Derived the symmetry group theorem for the Lin-Tsien equation.

Obtained conservation laws related to the Kac-Moody-Virasoro symmetry algebra.

Connected symmetry invariants to conservation laws up to second order.

Abstract

In this paper, We derive the symmetry group theorem to the Lin-Tsien equation by using the modified CK's direct method, from which we obtain the corresponding symmetry group. More importantly, conservation laws corresponding to the Kac-Moody-Virasoro symmetry algebra of Lin-Tsien equation is obtained up to second order group invariants.