Old and New Reductions of Dispersionless Toda Hierarchy
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Old and New Reductions of Dispersionless Toda Hierarchy
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| Creator |
Takasaki, K.
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| Description |
This paper is focused on geometric aspects of two particular types of finite-variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of ''Landau-Ginzburg potentials'' that play the role of reduced Lax functions. One of them is a generalization of Dubrovin and Zhang's trigonometric polynomial. The other is a transcendental function, the logarithm of which resembles the waterbag models of the dispersionless KP hierarchy. They both satisfy a radial version of the Löwner equations. Consistency of these Löwner equations yields a radial version of the Gibbons-Tsarev equations. These equations are used to formulate hodograph solutions of the reduced hierarchy. Geometric aspects of the Gibbons-Tsarev equations are explained in the language of classical differential geometry (Darboux equations, Egorov metrics and Combescure transformations). Flat coordinates of the underlying Egorov metrics are presented.
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| Date |
2019-02-19T18:21:19Z
2019-02-19T18:21:19Z 2012 |
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| Type |
Article
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| Identifier |
Old and New Reductions of Dispersionless Toda Hierarchy / K. Takasaki // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 37 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 35Q99; 37K10; 53B50; 53D45 DOI: http://dx.doi.org/10.3842/SIGMA.2012.102 http://dspace.nbuv.gov.ua/handle/123456789/149183 |
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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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