Related papers: The Semi Classical Maupertuis-Jacobi Correspondanc…
We study purely nonlocal Hamiltonian structures for systems of hydrodynamic type. In the case of a semi-Hamiltonian system, we show that such structures are related to quadratic expansions of the diagonal metrics naturally associated with…
In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine…
Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{\'e} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the…
We develop a microscopic model of mutual friction represented by the dissipative dynamics of a normal fluid flow which interacts with the helical normal modes of vortices comprising a lattice in thermal equilibrium. Such vortices are…
We study effects of electron correlation on the transport through a small interacting system connected to reservoirs using an effective Hamiltonian which describes the free quasi-particles of a Fermi liquid. The effective Hamiltonian is…
In a recent letter [Phys. Rev. Lett. {\bf 100}, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of…
We consider Hamiltonian systems restricted to the hypersurfaces of contact type and obtain a partial version of the Arnold-Liouville theorem: the system not need to be integrable on the whole phase space, while the invariant hypersurface is…
Many equations that arise in a physical context can be posed in the form of a Hamiltonian system, meaning that there is a symplectic structure on an appropriate phase space, and a Hamiltonian functional with respect to which time evolution…
Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…
We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasi-solvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasi-solvability of…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on…
The quasi-bound modes localized on stable periodic ray orbits of dielectric micro-cavities are constructed in the short-wavelength limit using the parabolic equation method. These modes are shown to coexist with irregularly spaced "chaotic"…
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the…
We explore the ground states of strongly interacting bosons in the vanishingly small and weak lattices using the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) which calculate numerically exact many-body wave function.…
A system of first-order differential-difference equations with time lag describes the formation of density waves, called as quasi-solitons for dissipative systems in this paper. For co-moving density waves, the system reduces to some…
We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the…
We review recent advances regarding the long-time dynamics of space-periodic water waves, focusing on 1) bifurcation of quasi-periodic solutions, both standing and traveling; 2) long-time well-posedness results; 3) modulational instability…
In this paper we study quasi-linear system of partial differential equations which describes the existence of the polynomial in momenta first integral of the integrable geodesic flow on 2-torus. We proved in [3] that this is a…
Motivated by the study of conditional stability of traveling waves, we give an elementary $H^2$ center stable manifold construction for quasilinear parabolic PDE, sidestepping apparently delicate regularity issues by the combination of a…