In this paper, reduced-order models (ROMs) are constructed for the Ablowitz-Ladik equation (ALE), an integrable semi-discretization of nonlinear Schrödinger (NLSE) with and without damping. Both ALEs non-canonical conservative dissipative Hamiltonian systems Poisson matrix depending quadratically on state variables, quadratic Hamiltonian. The full-order solutions obtained energy preserving midp...

Oscillatory instabilities in Hamiltonian anharmonic lattices are known to appear through Hamiltonian Hopf bifurcations of certain time-periodic solutions of multibreather type. Here, we analyze the basic mechanisms for this scenario by considering the simplest possible model system of this kind where they appear: the three-site discrete nonlinear Schrödinger model with periodic boundary conditi...

The low lying rotational resonance states of Ar-HCl van der Waals molecule in the vibrational ground state of HCl are calculated for several total angular momentum states within the model of a rigid rotor-atom system. The necessary scattering calculations are done by the finite range scattering wave function (FRSW) method [J. Chem. Phys. 99, 1057 (1993)] adopting energy independent auxiliary fu...

Discrete-time evolution operators in integrable quantum lattice models are sometimes more fundamental objects then Hamiltonians. In this paper we study an evolution operator for the one-dimensional integrable q-deformed Bose gas with XXZ-type impurities and find its spectrum. Evolution operators give a new interpretation of known integrable systems, for instance our system describes apparently ...

We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for arise as matrix elements propagator to evaluate length and area function with arbitrary starting ending points, expressing it rational combination determinants. Exploiting connection between random walks quantum exclusion statistics that we previously established, ...

In this paper a new discrete isospectral problem is constructed, from which a new Lax integrable discrete equation is generated and obtain its hierarchy structure. The Hamiltonian structures for the hierarchy of the Lax integrable discrete equation is established by using the trace identity which was proposed by Tu.

A graph is supereulerian if it has a spanning closed trail. For an integer r, let Q0(r) be the family of 3-edge-connected nonsupereulerian graphs of order at most r. For a graph G, define δL(G) = min{max{d(u), d(v)}| for any uv ∈ E(G)}. For a given integer p > 2 and a given real number , a graph G of order n is said to satisfy a Lai’s condition if δL(G) > np − . In this paper, we show that if G...