Singularity Analysis and Integrability of a Burgers-Type System of Foursov

TL;DR

This paper applies the Painleve test to a coupled Burgers-type system, confirming its C-integrability and linearizing transformation, and highlighting its rich symmetry structure.

Contribution

It demonstrates the integrability of Foursov's coupled Burgers system using Painleve analysis and identifies its linearizing transformation, expanding understanding of its mathematical properties.

Findings

System is C-integrable in the Calogero sense

Painleve test confirms integrability and linearization

System possesses infinitely many symmetries

Abstract

We apply the Painleve test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infinitely many commuting local generalized symmetries without any recursion operator. The Painleve analysis easily detects that this is a typical C-integrable system in the Calogero sense and rediscovers its linearizing transformation.