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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type
Peter J. Vassiliou Program in Mathematics and Statistics, University of Canberra, 2601 Australia
Аннотация:
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 ${\rm SL}(2)$ 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.
Ключевые слова:
wave map; Cauchy problem; Darboux integrable; Lie system; Lie reduction; explicit representation.
Поступила: 27 сентября 2012 г.; в окончательном варианте 12 марта 2013 г.; опубликована 18 марта 2013 г.
Образец цитирования:
Peter J. Vassiliou, “Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type”, SIGMA, 9 (2013), 024, 21 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma807 https://www.mathnet.ru/rus/sigma/v9/p24
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