Nonlocal conservation laws of the constant astigmatism equation

TL;DR

This paper develops a framework of nonlocal conservation laws for the constant astigmatism equation, revealing its invariance properties under reciprocal transformations and identifying independent potentials.

Contribution

It introduces a new system of nonlocal conservation laws for the constant astigmatism equation, expanding understanding of its integrability and symmetry structures.

Findings

Constructed a system of nonlocal conservation laws

Identified potentials independent modulo a Wronskian relation

Demonstrated closure under reciprocal transformations

Abstract

For the constant astigmatism equation, we construct a system of nonlocal conservation laws (an abelian covering) closed under the reciprocal transformations. We give functionally independent potentials modulo a Wronskian type relation.