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Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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| dc.contributor.author | Vassiliou, P.J. | |
| dc.date.accessioned | 2019-02-19T19:02:16Z | |
| dc.date.available | 2019-02-19T19:02:16Z | |
| dc.date.issued | 2013 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2010 Mathematics Subject Classification: 53A35; 53A55; 58A15; 58A20; 58A30 | |
| dc.identifier.other | DOI: http://dx.doi.org/10.3842/SIGMA.2013.024 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/149228 | |
| dc.description.abstract | 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. | uk_UA |
| dc.description.sponsorship | This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html. I’m grateful to the three anonymous referees for their close reading of the manuscript and for making suggestions which considerably improved the paper. I would like to acknowledge, with my thanks, the early involvement of Jordane Math´e for carefully working together through the calculations in Section 4 which formed a portion of his internship from the Ecole normale sup´erieure de Cachan, France. Much of the research for this paper was carried out while I was a Visiting Fellow at the Mathematical Sciences Institute of the Australian National University, Canberra. The hospitality of the MSI is gratefully acknowledged. In particular, I thank Mike Eastwood and the Dif ferential Geometry Group for stimulating discussions. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
