Nonlocal symmetries and conservation laws of the coupled Hirota equation

TL;DR

This paper explores nonlocal symmetries of the coupled Hirota equation, localizes them to Lie point symmetries, and derives conservation laws, enhancing understanding of its integrability properties.

Contribution

It introduces a method to localize nonlocal symmetries of the coupled Hirota equation and derives associated conservation laws, advancing symmetry analysis techniques.

Findings

Nonlocal symmetry obtained via the Lax pair.

Nonlocal symmetry successfully localized to Lie point symmetry.

Derived nonlocal conservation laws for the coupled Hirota equation.

Abstract

Using the lax pair, nonlocal symmetry of the coupled Hirota equation is obtained. By introducing an appropriate auxiliary dependent variable the nonlocal symmetry is successfully localized to a Lie point symmetry. For the closed prolongation, one-dimensional optimal systems and nonlocal conservation laws of the coupled Hirota equation are studied.