A systemic method to construct the high order nonlocal symmetries

TL;DR

This paper introduces a systematic approach for deriving high order nonlocal symmetries of nonlinear evolution equations using auxiliary systems, validated through multiple examples.

Contribution

It presents a novel systemic method for constructing high order nonlocal symmetries leveraging auxiliary systems, enhancing symmetry analysis techniques.

Findings

Successfully applied the method to several nonlinear evolution equations.

Demonstrated the effectiveness of the approach through concrete examples.

Provides a new tool for symmetry analysis in nonlinear dynamics.

Abstract

We propose a systemic method of applying the auxiliary systems of original equations to find the high order nonlocal symmetries of nonlinear evolution equation. In order to validate the effectiveness of the method, some examples are presented.