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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 063, 10 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.063 (Mi sigma91) 		 
This article is cited in 23 scientific papers (total in 23 papers)

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

Tadashi Kobayashia, Kouichi Todab

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
Full-text PDF (867 kB) Citations (23)
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DOI: https://doi.org/10.3842/SIGMA.2006.063
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.
Keywords: KdV equation with variable-coefficients; Painlevé test; higher-dimensional integrable systems.
Received: November 30, 2005; in final form June 17, 2006; Published online June 30, 2006
Bibliographic databases:
Document Type: Article
MSC: 37K10; 35Q53
Language: English
Citation: Tadashi Kobayashi, Kouichi Toda, “The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients”, SIGMA, 2 (2006), 063, 10 pp.
Citation in format AMSBIB
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\by Tadashi Kobayashi, Kouichi Toda
\paper The Painlev\'e Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with
Variable-Coefficients
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\yr 2006
\vol 2
\papernumber 063
\totalpages 10
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    • This publication is cited in the following 23 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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