Related papers: Discrete time Toda systems
We generalise the concept of duality to lattice equations. We derive a novel 3 dimensional lattice equation, which is dual to the lattice AKP equation. Reductions of this equation include Rutishauser's quotient-difference (QD) algorithm,…
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
We consider compositions of the transformations of the time variable and canonical transformations of the other coordinates, which map completely integrable system into other completely integrable system. Change of the time gives rise to…
We introduce the differential, integral, and variational delta-embeddings. We prove that the integral delta-embedding of the Euler-Lagrange equations and the variational delta-embedding coincide on an arbitrary time scale. In particular, a…
We study the interpolation analogue of the Hermite-Pad\'e type I approximation problem. We provide its determinant solution and we write down the corresponding integrable discrete system as an admissible reduction of Hirota's discrete…
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
Multidimensional consistency has emerged as a key integrability property for partial difference equations (P$\Delta$Es) defined on the "space-time" lattice. It has led, among other major insights, to a classification of scalar affine-linear…
We study properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. Specifically, we investigate the spectral behaviour of the corresponding Lax matrices when the number $N$ of degrees of…
This paper develops the theory of discrete Dirac reduction of discrete Lagrange-Dirac systems with an abelian symmetry group acting on the configuration space. We begin with the linear theory and, then, we extend it to the nonlinear setting…
It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that…
We study the discretization of Darboux integrable systems. The discretization is done using $x$-, $y$-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.
This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers stability and…
The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period $T$ yet mimic with good approximation, or even…
In this work, sample-based observability of linear discrete-time systems is studied. That is, we consider the case where the system output measurements are not available at every time instance. It is shown that some discrete-time systems…
The massive phase of two-layer integrable systems is studied by means of RSOS restrictions of affine Toda theories. A general classification of all possible integrable perturbations of coupled minimal models is pursued by an analysis of the…
Soliton models are used in elementary particle physics and nuclear physics to model extended objects such as nucleons, using effective field theories derived from more fundamental theories such as QCD. Computer simulation requires some sort…
The integration procedure for multidimensional cosmological models with multicomponent perfect fluid in spaces of constant curvature is developed. Reduction of pseudo-Euclidean Toda-like systems to the Euclidean ones is done. Some known…
Passing from a microscopic discrete lattice system with many degrees of freedom to a mesoscopic continuum system described by a few coarse-grained equations is challenging. The common folklore is to take the thermodynamic limit so that the…