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

Tadashi Kobayashi·Kouichi Toda
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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 Painleve 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.

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Tadashi Kobayashi, Kouichi Toda. 2006-06-30. The Painleve Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients. https://doi.org/10.3842/sigma.2006.063

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