Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type
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| Creator |
Vassiliou, P.J.
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| Description |
The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler-Lagrange equation for the energy functional is Darboux integrable. The time evolution of the Cauchy data is reduced to an ordinary differential equation of Lie type associated to SL(2) acting on a manifold of dimension 4. This is further reduced to the simplest Lie system: the Riccati equation. Lie reduction permits explicit representation formulas for various initial value problems. Additionally, a concise (hyperbolic) Weierstrass-type representation formula is derived. Finally, a number of open problems are framed.
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| Date |
2019-02-19T19:02:16Z
2019-02-19T19:02:16Z 2013 |
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| Type |
Article
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| Identifier |
Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type / P.J. Vassiliou // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 23 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 53A35; 53A55; 58A15; 58A20; 58A30 DOI: http://dx.doi.org/10.3842/SIGMA.2013.024 http://dspace.nbuv.gov.ua/handle/123456789/149228 |
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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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