Two-component integrable generalizations of Burgers equations with nondiagonal linearity

TL;DR

This paper classifies and analyzes new two-component Burgers-type systems with nondiagonal linearity, identifying integrable cases, symmetries, conservation laws, and bi-Poisson structures, advancing understanding of their mathematical properties.

Contribution

It introduces new integrable two-component Burgers systems with nondiagonal linearity, providing their symmetries, conservation laws, and bi-Poisson structures, which were not previously known.

Findings

New integrable systems with symmetries identified

Conservation laws found for some third-order systems

Bi-Poisson structures constructed for systems with conservation laws

Abstract

Two-component second and third-order Burgers type systems with nondiagonal constant matrix of leading order terms are classified for higher symmetries. New symmetry integrable systems with their master symmetries are obtained. Some third order systems are observed to possess conservation laws. Bi-Poisson structures of systems possessing conservation laws are given.