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

SIGMA 2 (2006), 063, 10 pages      nlin.SI/0606071      https://doi.org/10.3842/SIGMA.2006.063

The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients

Tadashi Kobayashi a and Kouichi Toda b
a) High-Functional Design G, LSI IP Development Div., ROHM CO., LTD., 21, Saiin Mizosaki-cho, Ukyo-ku, Kyoto 615-8585, Japan
b) Department of Mathematical Physics, Toyama Prefectural University, Kurokawa 5180, Imizu, Toyama, 939-0398, Japan

Received November 30, 2005, in final form June 17, 2006; Published online June 30, 2006

Abstract
The general KdV equation (gKdV) derived by T. Chou is one of the famous (1 + 1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable. In this paper a higher-dimensional gKdV equation, which is integrable in the sense of the Painlevé test, is presented. A transformation that links this equation to the canonical form of the Calogero-Bogoyavlenskii-Schiff equation is found. Furthermore, the form and similar transformation for the higher-dimensional modified gKdV equation are also obtained.

Key words: KdV equation with variable-coefficients; Painlevé test; higher-dimensional integrable systems.

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