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