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Steklov-Lyapunov type systems
In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m)×so(m). We show that the restriction of these systems onto some subvarieties of the orbit...
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| Format: | Default Preprint |
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2007
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| Online Access: | https://hdl.handle.net/2134/2763 |
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| _version_ | 1818176270119206912 |
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| author | Alexey V. Bolsinov Yu. Fedorov |
| author_facet | Alexey V. Bolsinov Yu. Fedorov |
| author_sort | Alexey V. Bolsinov (7159328) |
| collection | Figshare |
| description | In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m)×so(m). We show that the restriction of these systems onto some subvarieties of the orbits written in new matrix variables admits a new r × r matrix Lax representation in a generalized Gaudin form with a rational spectral parameter. In the case of rank 2 orbits a corresponding 2×2 La x pair for the reduced systems enables us to perform a separation of variables. |
| format | Default Preprint |
| id | rr-article-9382496 |
| institution | Loughborough University |
| publishDate | 2007 |
| record_format | Figshare |
| spelling | rr-article-93824962007-01-01T00:00:00Z Steklov-Lyapunov type systems Alexey V. Bolsinov (7159328) Yu. Fedorov (7160366) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m)×so(m). We show that the restriction of these systems onto some subvarieties of the orbits written in new matrix variables admits a new r × r matrix Lax representation in a generalized Gaudin form with a rational spectral parameter. In the case of rank 2 orbits a corresponding 2×2 La x pair for the reduced systems enables us to perform a separation of variables. 2007-01-01T00:00:00Z Text Preprint 2134/2763 https://figshare.com/articles/preprint/Steklov-Lyapunov_type_systems/9382496 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified Alexey V. Bolsinov Yu. Fedorov Steklov-Lyapunov type systems |
| title | Steklov-Lyapunov type systems |
| title_full | Steklov-Lyapunov type systems |
| title_fullStr | Steklov-Lyapunov type systems |
| title_full_unstemmed | Steklov-Lyapunov type systems |
| title_short | Steklov-Lyapunov type systems |
| title_sort | steklov-lyapunov type systems |
| topic | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/2763 |