The periodic b -equation and Euler equations on the circle

In this note we show that the periodic b -equation can only be realized as a Euler equation on the Lie group Diff ∞ ( S 1 ) of all smooth and orientation preserving diffeomorphisms on the circle if b = 2 , i.e., for the Camassa–Holm equation. In this case the inertia operator generating the metric o...

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Veröffentlicht in:	Journal of mathematical physics 2010-05, Vol.51 (5), p.053101-053101-6
Hauptverfasser:	Escher, Joachim, Seiler, Jörg
Format:	Artikel
Sprache:	eng
Schlagworte:	Eulers equations Exact sciences and technology Lie groups Mathematical methods in physics Mathematical models Mathematics Nonlinear equations Partial differential equations Physics Sciences and techniques of general use
Online-Zugang:	Volltext
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