Nonlocal symmetries of integrable two-field divergent evolutionary systems

TL;DR

This paper computes nonlocal symmetries for integrable two-field third-order evolutionary systems, derives associated nonevolutionary systems, and presents zero curvature representations for some of these new systems.

Contribution

It introduces a method to find nonlocal symmetries and zero curvature representations for new nonevolutionary systems related to integrable two-field evolutionary equations.

Findings

Computed nonlocal symmetries for integrable systems.

Derived new nonevolutionary systems from these symmetries.

Presented zero curvature representations for some of the new systems.

Abstract

Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each evolutionary system. Zero curvature representations for some new nonevolution systems are presented.