Discrete Lagrangian systems on the Virasoro group and Camassa-Holm family

Details Discrete Lagrangian systems on the Virasoro group and Camassa-Holm family Discrete Lagrangian systems on the Virasoro group and Camassa-Holm family

2002-09-19

arxiv.org/abs/math-ph/0209037v3

Nonlinearity 16 (2003), no.2, 683--688.

Physics

Mathematical Physics

6 pages, no figures, AMS-LaTeX. Version 2: minor changes. Version 3: minor changes

Scientific paper

10.1088/0951-7715/16/2/318

We show that the continuous limit of a wide natural class of the right-invariant discrete Lagrangian systems on the Virasoro group gives the family of integrable PDE's containing Camassa-Holm, Hunter-Saxton and Korteweg-de Vries equations. This family has been recently derived by Khesin and Misiolek as Euler equations on the Virasoro algebra for $H^1_{\alpha,\beta}$-metrics. Our result demonstrates a universal nature of these equations.

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