Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions
We consider the recursion operator approach to the soliton equations related to the generalized Zakharov-Shabat system on the algebra sl(n,C) in pole gauge both in the general position and in the presence of reductions. We present the recursion operators and discuss their geometric meaning as conjug...
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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/123456789/148684 |
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| Cite this: | Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions / A.B. Yanovski, G. Vilasi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 37 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862659656482029568 |
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| author | Yanovski, A.B. Vilasi, G. |
| author_facet | Yanovski, A.B. Vilasi, G. |
| citation_txt | Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions / A.B. Yanovski, G. Vilasi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 37 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider the recursion operator approach to the soliton equations related to the generalized Zakharov-Shabat system on the algebra sl(n,C) in pole gauge both in the general position and in the presence of reductions. We present the recursion operators and discuss their geometric meaning as conjugate to Nijenhuis tensors for a Poisson-Nijenhuis structure defined on the manifold of potentials.
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| first_indexed | 2025-12-02T09:49:41Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148684 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T09:49:41Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Yanovski, A.B. Vilasi, G. 2019-02-18T17:53:45Z 2019-02-18T17:53:45Z 2012 Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions / A.B. Yanovski, G. Vilasi // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 37 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q51; 37K05; 37K10 DOI: http://dx.doi.org/10.3842/SIGMA.2012.087 https://nasplib.isofts.kiev.ua/handle/123456789/148684 We consider the recursion operator approach to the soliton equations related to the generalized Zakharov-Shabat system on the algebra sl(n,C) in pole gauge both in the general position and in the presence of reductions. We present the recursion operators and discuss their geometric meaning as conjugate to Nijenhuis tensors for a Poisson-Nijenhuis structure defined on the manifold of potentials. The authors are grateful to A.V. Mikhailov and V.S. Gerdjikov for drawing their attention to
 the theory of the recursion operators in the presence of reductions and the problems related to it. We would like also to thank the referees who read carefully the manuscript and make number of remarks that helped to improve considerably the manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions Article published earlier |
| spellingShingle | Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions Yanovski, A.B. Vilasi, G. |
| title | Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions |
| title_full | Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions |
| title_fullStr | Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions |
| title_full_unstemmed | Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions |
| title_short | Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C) with and without Reductions |
| title_sort | geometric theory of the recursion operators for the generalized zakharov-shabat system in pole gauge on the algebra sl(n,c) with and without reductions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148684 |
| work_keys_str_mv | AT yanovskiab geometrictheoryoftherecursionoperatorsforthegeneralizedzakharovshabatsysteminpolegaugeonthealgebraslncwithandwithoutreductions AT vilasig geometrictheoryoftherecursionoperatorsforthegeneralizedzakharovshabatsysteminpolegaugeonthealgebraslncwithandwithoutreductions |