A New Class of Solvable Many-Body Problems
A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velo...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148447 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A New Class of Solvable Many-Body Problems / F. Calogero, G. Yi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 24 назв. — англ. |
Репозитарії
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nasplib_isofts_kiev_ua-123456789-148447 |
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Calogero, F. Yi, G. 2019-02-18T12:40:52Z 2019-02-18T12:40:52Z 2012 A New Class of Solvable Many-Body Problems / F. Calogero, G. Yi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 70F10; 70H06; 37J35; 37K10 DOI: http://dx.doi.org/10.3842/SIGMA.2012.066 https://nasplib.isofts.kiev.ua/handle/123456789/148447 A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velocity-dependent one-body and two-body forces) featuring several arbitrary coupling constants. The corresponding initial-value problems are solved by finding the eigenvalues of a time-dependent N×N matrix U(t) explicitly defined in terms of the initial positions and velocities of the N particles. Some of these models are asymptotically isochronous, i.e. in the remote future they become completely periodic with a period T independent of the initial data (up to exponentially vanishing corrections). Alternative formulations of these models, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited. This paper is a contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”. The full collection is available at http://www.emis.de/journals/SIGMA/SESSF2012.html. We would like to thank an unknown referee whose intervention allowed us to eliminate a mistake contained in the original version of our paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A New Class of Solvable Many-Body Problems Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A New Class of Solvable Many-Body Problems |
| spellingShingle |
A New Class of Solvable Many-Body Problems Calogero, F. Yi, G. |
| title_short |
A New Class of Solvable Many-Body Problems |
| title_full |
A New Class of Solvable Many-Body Problems |
| title_fullStr |
A New Class of Solvable Many-Body Problems |
| title_full_unstemmed |
A New Class of Solvable Many-Body Problems |
| title_sort |
new class of solvable many-body problems |
| author |
Calogero, F. Yi, G. |
| author_facet |
Calogero, F. Yi, G. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velocity-dependent one-body and two-body forces) featuring several arbitrary coupling constants. The corresponding initial-value problems are solved by finding the eigenvalues of a time-dependent N×N matrix U(t) explicitly defined in terms of the initial positions and velocities of the N particles. Some of these models are asymptotically isochronous, i.e. in the remote future they become completely periodic with a period T independent of the initial data (up to exponentially vanishing corrections). Alternative formulations of these models, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148447 |
| citation_txt |
A New Class of Solvable Many-Body Problems / F. Calogero, G. Yi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 24 назв. — англ. |
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2025-12-07T19:19:37Z |
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