arXiv subjects

A. V. Penskoi

Publications and source records attributed to A. V. Penskoi.

3 recordsLinked to original sources

arXiv2003

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

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.

math-ph↗

arXiv2000

On algebro-geometric Poisson brackets for the Volterra lattice

A generalization of the theory of algebro-geometric Poisson brackets on the space of finite-gap Schroedinger operators, developped by S. P. Novikov and A. P. Veselov, to the case of periodic zero-diagonal difference operators of second order is proposed. A necessary and sufficient condition for such a bracket to be compatible with higher Volterra flows is found.

math-ph↗

arXiv2000

The Volterra lattice as a gradient flow

The Volterra lattice is considered. New gradient interpretation for this dynamical system is proposed. This interpretation seems to be more natural than existing ones.

math-ph↗