Related papers: Lax representation of the hyperbolic van Diejen dy…
Following recent experiments on ultracold dual superflows, we model in this work the dynamics of two harmonically trapped counterflowing superfluids. Using complementary analytical and numerical approaches, we study the shedding of…
We suggest a new model for the dynamics of a suspension bridge through a system of nonlinear nonlocal hyperbolic differential equations. The equations are of second and fourth order in space and describe the behavior of the main components…
A system of replicators with Hebbian random couplings is studied using dynamical methods. The self-reproducing species are here characterized by a set of binary traits and interact based on complementarity. In the case of an extensive…
We consider a hierarchy of many-particle systems on the line with polynomial potentials separable in parabolic coordinates. The first non-trivial member of this hierarchy is a generalization of an integrable case of the H\'enon-Heiles…
We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton-Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied…
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is…
We study the dynamics of Einstein's equations in Ashtekar's variables from the point of view of the theory of hyperbolic systems of evolution equations. We extend previous results and show that by a suitable modification of the Hamiltonian…
We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax pair corresponding to a given nonlinear equation is found…
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…
In order to address the theoretical challenges arising from the dependence structure of ranks in Spearman's footrule correlation coefficient, we propose two asymptotic representations to approximate the distribution of this coefficient…
We construct so called Darboux matrices and fundamental solutions in the important case of the generalised Hamiltonian (or canonical) systems depending rationally on the spectral parameter. A wide class of explicit solutions is obtained in…
Inspired by the recent creation of the honeycomb optical lattice and the realization of the Mott insulating state in a square lattice by shaking, we study here the shaken honeycomb optical lattice. For a periodic shaking of the lattice, a…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
The aim of this paper is to apply direct methods to the study of integrals that appear naturally in Statistical Mechanics and Euclidean Field Theory. We provide weighted estimates leading to the exponential decay of the two-point…
This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect…
In this paper, the semiclassical limit of Davey-Stewartson systems are studied. It shows that these dispersionless limited integrable systems of hydrodynamic type, which are defined as dDS (dispersionless Davey-Stewartson) systems, are…
An extension of the Kinetic Ising model with nonuniform coupling constants on a one-dimensional lattice with boundaries is investigated, and the relaxation of such a system towards its equilibrium is studied. Using a transfer matrix method,…
A systematic method to obtain strong coupling expansions for scattering quantities in Hamiltonian lattice field theories is presented. I develop the conceptual ideas by means of the Hamiltonian field theory analogue of the Ising model, in…
This thesis presents our results on Liouville integrable systems of Calogero-Ruijsenaars type: 1. We prove an explicit formula providing canonical spectral coordinates for the rational Calogero-Moser system. 2. We explore action-angle…
We describe a linear homopolymer using a Grand Canonical ensemble formalism, a statistical representation that is very convenient for formal manipulations. We investigate the properties of a system where only next neighbor interactions and…