Coverings over Lax integrable equations and their nonlocal symmetries

TL;DR

This paper constructs nonlocal conservation laws and describes the symmetry algebras for the 3D rdDym equation using Lax representations with non-removable parameters.

Contribution

It introduces two hierarchies of nonlocal conservation laws and characterizes their symmetry algebras, advancing understanding of integrable equations with nonlocal structures.

Findings

Two hierarchies of nonlocal conservation laws are constructed.

The algebras of nonlocal symmetries are described for the coverings.

The approach uses Lax representations with non-removable parameters.

Abstract

Using the Lax representation with non-removable parameter, we construct two hierarchies of nonlocal conservation laws for the 3D rdDym equation $u_{ty} = u_xu_{xy} - u_yu_{xx}$ and describe the algebras of nonlocal symmetries in the corresponding coverings.