Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 7 (2011), 002, 5 pages      arXiv:1010.5709      http://dx.doi.org/10.3842/SIGMA.2011.002

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

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

Received October 28, 2010, in final form December 24, 2010; Published online January 04, 2011

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.

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

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