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The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients
Інший ID:
2000 Mathematics Subject Classification: 37K10; 35Q53
Посилання:
The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients / T. Kobayashi, K. Toda // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 70 назв. — англ.
Підтримка:
Many helpful discussions with Drs. Y. Ishimori, A. Nakamula, T. Tsuchida, S. Tsujimoto, Professors Y. Nakamura and P.G. Est´evez are acknowledged. One of the authors (K.T.) would like to thank Professor X.-B. Hu and his graduate students for kind hospitality and useful discussions during his stay at the Chinese Academy of Sciences (Beijing, China) in 2005, where part of this study has been done. The authors wish to extend their thanks to anonymous referees for their helpful and critical comments as this paper took shape. This work was supported by the First-Bank of Toyama Scholarship Foundation and in part by Grant-in-Aid for Scientific Research (#15740242) from the Ministry of Education, Culture, Sports, Science and Technology.
Дата:
2006
Переглядів:
491
Завантажень:
267
Анотація:
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.
