Multidimensional Toda Lattices: Continuous and Discrete Time
In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the orthogonal polynomial approach for the continuous and discrete Tod...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147750 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Multidimensional Toda Lattices: Continuous and Discrete Time / A.I. Aptekarev, M. Derevyagin, H. Miki, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712471282778112 |
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| author | Aptekarev, A.I. Derevyagin, M. Miki, H. Van Assche, W. |
| author_facet | Aptekarev, A.I. Derevyagin, M. Miki, H. Van Assche, W. |
| citation_txt | Multidimensional Toda Lattices: Continuous and Discrete Time / A.I. Aptekarev, M. Derevyagin, H. Miki, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the orthogonal polynomial approach for the continuous and discrete Toda lattices to the case of multiple orthogonal polynomials.
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| first_indexed | 2025-12-07T17:38:01Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147750 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:38:01Z |
| publishDate | 2016 |
| publisher | Інститут математики НАН України |
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| spelling | Aptekarev, A.I. Derevyagin, M. Miki, H. Van Assche, W. 2019-02-15T19:08:57Z 2019-02-15T19:08:57Z 2016 Multidimensional Toda Lattices: Continuous and Discrete Time / A.I. Aptekarev, M. Derevyagin, H. Miki, W. Van Assche // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 56 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 42C05; 37K10; 39A14; 65Q10 DOI:10.3842/SIGMA.2016.054 https://nasplib.isofts.kiev.ua/handle/123456789/147750 In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the orthogonal polynomial approach for the continuous and discrete Toda lattices to the case of multiple orthogonal polynomials. This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
 The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
 A.I. Aptekarev was supported by grant RScF-14-21-00025. M. Derevyagin thanks the hospitality
 of Department of Mathematics of KU Leuven, where his part of the research was initiated while
 he was a postdoc there. M. Derevyagin and W. Van Assche gratefully acknowledge the support
 of FWO Flanders project G.0934.13, KU Leuven research grant OT/12/073 and the Belgian
 Interuniversity Attraction Poles programme P07/18. H. Miki was supported by JSPS KAKENHI
 Grant Number 15K17561. Also, M. Derevyagin and H. Miki are grateful to S. Tsujimoto,
 L. Vinet, A. Zhedanov for valuable discussions and comments. Finally, all the authors thank
 the anonymous referees for their careful reading of the manuscript and for their remarks that
 improved the presentation of the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multidimensional Toda Lattices: Continuous and Discrete Time Article published earlier |
| spellingShingle | Multidimensional Toda Lattices: Continuous and Discrete Time Aptekarev, A.I. Derevyagin, M. Miki, H. Van Assche, W. |
| title | Multidimensional Toda Lattices: Continuous and Discrete Time |
| title_full | Multidimensional Toda Lattices: Continuous and Discrete Time |
| title_fullStr | Multidimensional Toda Lattices: Continuous and Discrete Time |
| title_full_unstemmed | Multidimensional Toda Lattices: Continuous and Discrete Time |
| title_short | Multidimensional Toda Lattices: Continuous and Discrete Time |
| title_sort | multidimensional toda lattices: continuous and discrete time |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147750 |
| work_keys_str_mv | AT aptekarevai multidimensionaltodalatticescontinuousanddiscretetime AT derevyaginm multidimensionaltodalatticescontinuousanddiscretetime AT mikih multidimensionaltodalatticescontinuousanddiscretetime AT vanasschew multidimensionaltodalatticescontinuousanddiscretetime |