The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients
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...
Збережено в:
| Дата: | 2006 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146104 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-146104 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1461042019-02-08T01:23:05Z The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients Kobayashi, T. Toda, K. 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. 2006 Article 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. 1815-0659 2000 Mathematics Subject Classification: 37K10; 35Q53 http://dspace.nbuv.gov.ua/handle/123456789/146104 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Kobayashi, T. Toda, K. |
| spellingShingle |
Kobayashi, T. Toda, K. The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kobayashi, T. Toda, K. |
| author_sort |
Kobayashi, T. |
| title |
The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients |
| title_short |
The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients |
| title_full |
The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients |
| title_fullStr |
The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients |
| title_full_unstemmed |
The Painlevé Test and Reducibility to the Canonical Forms for Higher-Dimensional Soliton Equations with Variable-Coefficients |
| title_sort |
painlevé test and reducibility to the canonical forms for higher-dimensional soliton equations with variable-coefficients |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146104 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT kobayashit thepainlevetestandreducibilitytothecanonicalformsforhigherdimensionalsolitonequationswithvariablecoefficients AT todak thepainlevetestandreducibilitytothecanonicalformsforhigherdimensionalsolitonequationswithvariablecoefficients AT kobayashit painlevetestandreducibilitytothecanonicalformsforhigherdimensionalsolitonequationswithvariablecoefficients AT todak painlevetestandreducibilitytothecanonicalformsforhigherdimensionalsolitonequationswithvariablecoefficients |
| first_indexed |
2023-05-20T17:23:50Z |
| last_indexed |
2023-05-20T17:23:50Z |
| _version_ |
1796153201280417792 |