We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid Q that are cut out by algebraic surfaces in R. Such geodesics are either connectedâ€¦ (More)

This papers studies discrete nonholonomic mechanical systems whose configuration space is a Lie group G Assuming that the discrete Lagrangian and constraints are left-invariant, the discreteâ€¦ (More)

The algebraicâ€“geometric approach is extended to study evolution equations associated with the energy-dependent SchrÃ¶dinger operators having potentials with poles in the spectral parameter, inâ€¦ (More)

We consider a class of dynamical systems on a compact Lie group G with a left-invariant metric and right-invariant nonholonomic constraints (so-called LR systems) and show that, under a genericâ€¦ (More)

This letter presents some special features of a class of integrable PDEâ€™s admitting billiard-type solutions, which set them apart from equations whose solutions are smooth, such as the KdV equation.â€¦ (More)

The celebrated problem of a non-homogeneous sphere rolling over a horizontal plane was proved to be integrable and was reduced to quadratures by Chaplygin. Applying the formalism of variationalâ€¦ (More)

Algebraic geometrical solutions of a new shallow-water equation and Dymtype equation are studied in connection with Hamiltonian flows on nonlinear subvarieties of hyperelliptic Jacobians. Theseâ€¦ (More)

PACS numbers 05.45.Yv, 03.40.Gc, 11.10.Ef, 68.10.-m, AMS Subject Classification 58F07, 70H99, 76B15 Research partially supported by NSF grant DMS 9626672 and NATO grant CRG 950897. Research supportedâ€¦ (More)

We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary conditions for theirâ€¦ (More)

We show that the m-dimensional Eulerâ€“Manakov top on soâˆ—(m) can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety VÌ„(k,m), and presentâ€¦ (More)