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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148447 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730285387350016 |
|---|---|
| author | Calogero, F. Yi, G. |
| author_facet | Calogero, F. Yi, G. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-07T19:19:37Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148447 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:19:37Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | A New Class of Solvable Many-Body Problems Calogero, F. Yi, G. |
| title | 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_short | A New Class of Solvable Many-Body Problems |
| title_sort | new class of solvable many-body problems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148447 |
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