The system of two parabolic equations as an integrable system

TL;DR

This paper introduces a new integrable system of two nonlinear parabolic PDEs, equivalent to Burgers equations, highlighting its potential significance in mathematical physics and integrability theory.

Contribution

It presents a novel, apparently unstudied system of two parabolic equations that is shown to be integrable via its equivalence to Burgers equations.

Findings

The system is shown to be integrable.

It is equivalent to two Burgers equations.

The system is potentially of independent interest.

Abstract

In this paper we present a system of two nonlinear partial differential equations of the second order, depending on the time and one spatial coordinate. It can be written as a system of two Burgers equations, which allows one to immediately conclude that it is integrable. This system seems to be new, and its consideration can be of independent interest.