Lie point symmetries and conservation laws for a Gardner type system

TL;DR

This paper identifies the Lie point symmetries of a Gardner type system, proves its nonlinear self-adjointness, and constructs associated conservation laws using Ibragimov's Theorem.

Contribution

It introduces the symmetry analysis and conservation law construction for a Gardner type system, highlighting its nonlinear self-adjointness, which is a novel application.

Findings

Lie point symmetries are determined for the system.

The system is shown to be nonlinear self-adjoint.

Conservation laws are constructed using Ibragimov's Theorem.

Abstract

We determine the Lie point symmetries of a Gardner type system and establish its nonlinear self-adjointness. We then construct conservation laws via Ibragimov's Theorem.