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math-ph2002★ 1 cited
Canonically conjugate variables for the periodic Camassa-Holm equation
Alexei V. Penskoi
The Camassa-Holm shallow water equation is known to be Hamiltonian with respect to two compatible Poisson brackets. A set of conjugate variables is constructed for both brackets us…
math-ph2002★ 2 cited
Discrete Lagrangian systems on the Virasoro group and Camassa-Holm family
A. V. Penskoi, A. P. Veselov
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 C…
math-ph2002★ 6 cited
Lagrangian time-discretization of the Hunter-Saxton equation
Alexei V. Penskoi
We study Lagrangian time-discretizations of the Hunter-Saxton equation. Using the Moser-Veselov approach, we obtain such discretizations defined on the Virasoro group and on the gr…