Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations

TL;DR

This paper develops gauge-invariant formulations for several (2+1)-dimensional integrable nonlinear equations, revealing new insights and transformations among these systems.

Contribution

It introduces gauge-invariant forms for key 2D integrable systems and explores Miura-type transformations between different gauges, advancing understanding of their interrelations.

Findings

Derived new gauge-invariant forms for integrable systems.

Connected various well-known 2D integrable equations through these forms.

Explored transformations linking equations in different gauges.

Abstract

We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges.