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

A. V. Penskoi·A. P. Veselov
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Abstract

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 $H^1_{α,β}$-metrics. Our result demonstrates a universal nature of these equations.

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A. V. Penskoi, A. P. Veselov. 2003-01-14. Discrete Lagrangian systems on the Virasoro group and Camassa-Holm family. https://doi.org/10.1088/0951-7715%2F16%2F2%2F318

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