Dynamical Studies of Equations from the Gambier Family
We consider the hierarchy of higher-order Riccati equations and establish their connection with the Gambier equation. Moreover we investigate the relation of equations of the Gambier family to other nonlinear differential systems. In particular we explore their connection to the generalized Ermakov-...
Збережено в:
| Дата: | 2011 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146785 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Dynamical Studies of Equations from the Gambier Family / P. Guha, A. Ghose Choudhury, P. Guha // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 23 назв. — англ. |
Репозитарії
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irk-123456789-146785 |
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irk-123456789-1467852019-02-12T01:24:23Z Dynamical Studies of Equations from the Gambier Family Guha, P. Ghose Choudhury, A. Grammaticos, B. We consider the hierarchy of higher-order Riccati equations and establish their connection with the Gambier equation. Moreover we investigate the relation of equations of the Gambier family to other nonlinear differential systems. In particular we explore their connection to the generalized Ermakov-Pinney and Milne-Pinney equations. In addition we investigate the consequence of introducing Okamoto's folding transformation which maps the reduced Gambier equation to a Liénard type equation. Finally the conjugate Hamiltonian aspects of certain equations belonging to this family and their connection with superintegrability are explored. 2011 Article Dynamical Studies of Equations from the Gambier Family / P. Guha, A. Ghose Choudhury, P. Guha // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 23 назв. — англ. 1815-0659 http://dspace.nbuv.gov.ua/handle/123456789/146785 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 |
We consider the hierarchy of higher-order Riccati equations and establish their connection with the Gambier equation. Moreover we investigate the relation of equations of the Gambier family to other nonlinear differential systems. In particular we explore their connection to the generalized Ermakov-Pinney and Milne-Pinney equations. In addition we investigate the consequence of introducing Okamoto's folding transformation which maps the reduced Gambier equation to a Liénard type equation. Finally the conjugate Hamiltonian aspects of certain equations belonging to this family and their connection with superintegrability are explored. |
| format |
Article |
| author |
Guha, P. Ghose Choudhury, A. Grammaticos, B. |
| spellingShingle |
Guha, P. Ghose Choudhury, A. Grammaticos, B. Dynamical Studies of Equations from the Gambier Family Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Guha, P. Ghose Choudhury, A. Grammaticos, B. |
| author_sort |
Guha, P. |
| title |
Dynamical Studies of Equations from the Gambier Family |
| title_short |
Dynamical Studies of Equations from the Gambier Family |
| title_full |
Dynamical Studies of Equations from the Gambier Family |
| title_fullStr |
Dynamical Studies of Equations from the Gambier Family |
| title_full_unstemmed |
Dynamical Studies of Equations from the Gambier Family |
| title_sort |
dynamical studies of equations from the gambier family |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146785 |
| citation_txt |
Dynamical Studies of Equations from the Gambier Family / P. Guha, A. Ghose Choudhury, P. Guha // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 23 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:25:49Z |
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2023-05-20T17:25:49Z |
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