相关论文: Discrete time Bogoyavlensky lattices

We develop a systematic procedure of finding integrable ''relativistic'' (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First,…

Continuous time (CT) and discrete time (DT) linear time invariant (LTI) systems are commonly introduced through distinct mathematical formalisms, which can obscure their underlying dynamical equivalence. This tutorial presents a unified…

We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…

This paper discusses energy-conserving time-discretizations for finite element particle-in-cell discretizations of the Vlasov--Maxwell system. A geometric spatially discrete system can be obtained using a standard particle-in-cell…

A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…

We propose the systematic construction of classical and quantum two dimensional space-time lattices primarily based on algebraic considerations, i.e. on the existence of associated r-matrices and underlying spatial and temporal classical…

The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…

We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets…

A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…

Some applications of the odd Poisson bracket developed by Kharkov's theorists are represented, including the reformulation of classical Hamiltonian dynamics, the description of hydrodynamics as a Hamilton system by means of the odd bracket…

We revisit the canonical continuous-time and discrete-time matrix algebraic and matrix differential equations that play a central role in Lyapunov based stability arguments. The goal is to generalize and extend these types of equations and…

An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…

In this paper, we present Poisson brackets of certain classes of mappings obtained as general periodic reductions of integrable lattice equations. The Poisson brackets are derived using the so called Ostrogradsky transformation.

We study several numerical discretization techniques for the one-space plus one-time dimensional Dirac equation, including finite difference and space-time finite element methods. Two finite difference schemes and several space-time finite…

We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…

An algebra isomorphism between algebras of matrices and difference operators is used to investigate the discrete integrable hierarchy. We find local and non-local families of R-matrix solutions to the modified Yang-Baxter equation. The…

We present two types of systems of differential equations that can be derived from a set of discrete integrable systems which we call the closed geometric crystal chains. One is a kind of extended Lotka-Volterra systems, and the other seems…

We study integrable hierarchies associated with spectral problems of the form $P\psi=\lambda Q\psi$ where $P,Q$ are difference operators. The corresponding nonlinear differential-difference equations can be viewed as inhomogeneous…

We study two families of (matrix versions of) generalized Volterra (or Bogoyavlensky) lattice equations. For each family, the equations arise as reductions of a partial differential-difference equation in one continuous and two discrete…

Consider the resolvent problem associated with the linearized viscous flow around a rotating body. Within a setting of classical Sobolev spaces, this problem is not well posed on the whole imaginary axis. Therefore, a framework of…