Sergei Sakovich, “Singularity Analysis and Integrability of a Burgers-Type System of Foursov”, SIGMA, 2011, Volume 7,002, 5 pp.

This article is cited in 2 papers

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

Sergei Sakovich^ab

^a Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
^b Institute of Physics, National Academy of Sciences, 220072 Minsk, Belarus

Abstract: We apply the Painlevé 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 Painlevé analysis easily detects that this is a typical $C$-integrable system in the Calogero sense and rediscovers its linearizing transformation.

Keywords: coupled Burgers-type equations; Painlevé test for integrability.

MSC: 35K55; 37K10

Received: October 28, 2010; in final form December 24, 2010; Published online January 4, 2011

Language: English

DOI: 10.3842/SIGMA.2011.002