Hamiltonian Flows of Curves in G/SO(N) and Vector Soliton Equations of mKdV and Sine-Gordon Type
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Hamiltonian Flows of Curves in G/SO(N) and Vector Soliton Equations of mKdV and Sine-Gordon Type
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| Creator |
Anco, S.C.
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| Description |
The bi-Hamiltonian structure of the two known vector generalizations of the mKdV hierarchy of soliton equations is derived in a geometrical fashion from flows of non-stretching curves in Riemannian symmetric spaces G/SO(N). These spaces are exhausted by the Lie groups G = SO(N+1),SU(N). The derivation of the bi-Hamiltonian structure uses a parallel frame and connection along the curve, tied to a zero curvature Maurer-Cartan form on G, and this yields the mKdV recursion operators in a geometric vectorial form. The kernel of these recursion operators is shown to yield two hyperbolic vector generalizations of the sine-Gordon equation. The corresponding geometric curve flows in the hierarchies are described in an explicit form, given by wave map equations and mKdV analogs of Schrödinger map equations.
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| Date |
2019-02-07T20:34:29Z
2019-02-07T20:34:29Z 2006 |
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| Type |
Article
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| Identifier |
Hamiltonian Flows of Curves in G/SO(N) and Vector Soliton Equations of mKdV and Sine-Gordon Type / S.C. Anco // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 37K05; 37K10; 37K25; 35Q53; 53C35 http://dspace.nbuv.gov.ua/handle/123456789/146182 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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