Related papers: Degenerately Integrable Systems
The Mishchenko-Fomenko theorem on superintegrable Hamiltonian systems is generalized to superintegrable Hamiltonian systems with noncompact invariant submanifolds. It is formulated in the case of globally superintegrable Hamiltonian systems…
An alternative Lagrangian definition of an integrable defect is provided and analyzed. The new approach is sufficiently broad to allow a description of defects within the Tzitzeica model, which was not possible in previous approaches, and…
The problem of finding most general form of the classical integrable relativistic models of many-body interaction of the $BC_{n}$ type is considered. In the simplest nontrivial case of $n=2$,the extra integral of motion is presented in…
Based on the Kupershmidt deformation for any integrable bi-Hamiltonian systems presented in [4], we propose the generalized Kupershmidt deformation to construct new systems from integrable bi-Hamiltonian systems, which provides a…
We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the…
Continuum mechanics can be formulated in the Lagrangian frame (addressing motion of individual continuum particles) or in the Eulerian frame (addressing evolution of fields in an inertial frame). There is a canonical Hamiltonian structure…
Relativistic Hamiltonian equations describing a motion of a point mass in an arbitrary homogeneous potential are considered. For the first time, the necessary integrability conditions for integrability in the Liouville sense for this class…
This article is the first one in a suite of three articles exploring connections between dynamical systems of St\"{a}ckel-type and of Painlev\'{e}- type. In this article we present a deformation of autonomous St\"{a}ckel-type systems to…
We study the optimal design of numerical integrators for dissipative systems, for which there exists an underlying thermodynamic structure known as GENERIC (general equation for the nonequilibrium reversible-irreversible coupling). We…
We give a natural notion of nondegeneracy for singular points of integrable non-Hamiltonian systems, and show that such nondegenerate singularities are locally geometrically linearizable and deformation rigid in the analytic case. We…
We present and develop a recursion scheme to construct joint eigenfunctions for the commuting analytic difference operators associated with the integrable N-particle systems of hyperbolic relativistic Calogero-Moser type. The scheme is…
The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of such integrals means that the system…
The integrable systems known as "AKS systems" admit a natural formulation in terms of a Hamiltonian picture. The Lagrangian side of these systems are far less known; a version in these terms can be found in a work of Feher et al. The…
We study classical integrable systems based on the Alekseev-Meinrenken dynamical r-matrices corresponding to automorphisms of self-dual Lie algebras, ${\cal G}$. We prove that these r-matrices are uniquely characterized by a non-degeneracy…
In this paper, we discuss some results on integrable Hamiltonian systems with two degrees of freedom. We revisit the much-studied problem of the two-dimensional harmonic oscillator and discuss its (super)integrability in the light of a…
The existence of strong solutions to general class of strongly coupled parabolic systems will be discussed. These systems can be degenerate or singular as boundedness of theirs solutions are unavailable and not assummed. The results greatly…
We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue…
The Author shows how to construct a class of Lagrangians for relativistic dynamical systems described by position and a single spinor. One arrives to it by imposing three requirements: 1) Hamilton action should be reparametrization…
Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri…
It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the…