Related papers: Integrability properties of Motzkin polynomials
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…
In this paper, we present a general scheme to construct integrable systems based on realization in the coboundary dynamical Poisson groupoids of Etingof and Varchenko. We also present a factorization method for solving the Hamiltonian…
We consider $\mathcal{PT}$-symmetric ring-like arrays of optical waveguides with purely nonlinear gain and loss. Regardless of the value of the gain-loss coefficient, these systems are protected from spontaneous $\mathcal{PT}$-symmetry…
We discuss a general approach permitting the identification of a broad class of sets of Poisson-commuting Hamiltonians, which are integrable in the sense of Liouville. It is shown that all such Hamiltonians can be solved explicitly by a…
In this methodological review, we discuss the fundamental concepts of the theory of integral invariants. This theory originated with Poincare and Cartan \cite{Koz, Kart} and was further developed by Kozlov \cite{int_K}. We demonstrate how…
Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi method. Integration of a set of equations of motion and the action function is discussed. It is shown that we have two types of integrable systems: a) ${\it…
It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold.…
Integrable structures arise in general relativity when the spacetime possesses a pair of commuting Killing vectors admitting 2-spaces orthogonal to the group orbits. The physical interpretation of such spacetimes depends on the norm of the…
The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…
We show that Jacobi fields of a completely integrable Hamiltonian system of m degrees of freedom also make up a completely integrable system. They provide m additional first integrals which characterize a relative motion.
In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover,…
We briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in ${\bf R}^3$, its connection with a specific Gaudin XXX system, as well as the generalisation to $su(r), r>2$. Then we…
Hamiltonian Poisson integrators are Poisson integrators that admit a modified Hamiltonian. In this article, we illustrate the importance of the existence of a modified Hamiltonian for Poisson integrators in the context of integrable and…
We observe that the modular class of a Poisson-Nijhenhuis manifold has a canonical representative and that, under a cohomological assumption, this vector field is bi-hamiltonian. In many examples the associated hierarchy of flows reproduces…
Different classes of physical systems with sizeable electron-phonon coupling and lattice distortions present anomalous resistivity behaviors versus temperature. We study a molecular lattice Hamiltonian in which polaronic charge carriers…
We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic…
Hamiltonian systems are a classical example in the ergodic theory of flows with an invariant measure. In this matter, we present a brief introduction to measure theory and prove the Poincare recurrence theorem to present the conditions for…
The strict relation between some class of multiboson hamiltonian systems and the corresponding class of orthogonal polynomials is established. The correspondence is used effectively to integrate the systems. As an explicit example we…
Phase space of a characteristic Hamiltonian system is a symplectic leaf of a factorizable Poisson Lie group. Its Hamiltonian is a restriction to the symplectic leaf of a function on the group which is invariant with respect to conjugations.…
A novel canonical Hamiltonian formalism is developed for long internal waves in a rotating environment. This includes the effects of background vorticity and shear on the waves. By restricting consideration to flows in hydrostatic balance,…