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

TL;DR

This paper introduces gauge-invariant formulations of certain (2+1)-dimensional integrable nonlinear equations, showing how different gauges yield known and new integrable systems, and explores transformations between them.

Contribution

It presents new gauge-invariant forms of 2D integrable equations and analyzes gauge transformations and Miura-type relations among them.

Findings

New gauge-invariant forms of integrable equations

Derivation of known and new equations from these forms

Analysis of gauge transformations and Miura relations

Abstract

New manifestly gauge-invariant forms of two-dimensional generalized dispersive long-wave and Nizhnik-Veselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous two-dimensional generalization of dispersive long-wave system of equations, Nizhnik-Veselov-Novikov and modified Nizhnik-Veselov-Novikov equations and other known and new integrable nonlinear equations arise. Miura-type transformations between nonlinear equations in different gauges are considered.