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Hamiltonian systems discrete-time approximation: Losslessness, passivity and composability
Systems & Control Letters, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aoues, Said +3 more
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Hamiltonian structure of discrete soliton systems
Journal of Physics A: Mathematical and General, 2002Summary: We describe an approach for investigating the Hamiltonian structures of the lattice isospectral evolution equations associated with a general discrete spectral problem. By using the so-called implicit representations of the isospectral flows, we demonstrate the existence of the recursion operator \(L\), which is a strong and hereditary ...
Zhang, Dajun, Chen, Dengyuan
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Discrete Linear Hamiltonian Systems
1996This chapter is an introduction to Martin Bohner’s approach to the discrete linear Hamiltonian system $$\begin{array}{*{20}{c}} {\Delta y\left( t \right) = A\left( t \right)y\left( {t + 1} \right) + B\left( t \right)z\left( t \right)} \\ {\Delta z\left( t \right) = C\left( t \right)y\left( {t + 1} \right) - A*\left( t \right)z\left( t \right ...
Calvin D. Ahlbrandt, Allan C. Peterson
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Multipulses in discrete Hamiltonian nonlinear systems
Physical Review E, 2001In this work, the behavior of multipulses in discrete Hamiltonian nonlinear systems is investigated. The discrete nonlinear Schrödinger equation is used as the benchmark system for this study. A singular perturbation methodology as well as a variational approach are implemented in order to identify the dominant factors in the discrete problem.
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On the Periodic Solutions of Discrete Hamiltonian Systems
AIP Conference Proceedings, 2009Almost all numerical methods for solving conservative problems cannot avoid a more or less perceptible drift phenomenon. Considering that the drift would be absent on a periodic or quasi‐periodic solution, one way to eliminate such unpleasant phenomenon is to look for discrete periodic or quasi‐periodic solutions.
Lidia Aceto +4 more
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Discretization of Hamiltonian Systems and Intersection Theory
Theoretical and Mathematical Physics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multiple periodic solutions for discrete Hamiltonian systems
Nonlinear Analysis: Theory, Methods & Applications, 2007This work deals with the discrete Hamiltonian system \[ \begin{cases} \Delta u_1(n)=-H_{u_2}(n,u_1(n+1),u_2(n)),\\ \Delta u_2(n)=H_{u_1}(n,u_1(n+1),u_2(n)), &n\in \mathbb Z,\end{cases}\tag{1} \] where \(u_1,\,u_2\in \mathbb R^N\) and \(\Delta u_i(n)=u_i(n+1)-u_i(n)\), \(i=1,2\).
Yu, Jianshe, Bin, Honghua, Guo, Zhiming
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Localized Excitations in Discrete Hamiltonian Systems
1994The modification of soliton properties (e. g. of kinks and breathers) in discrete systems has been studied over a rather long period of time1. Recently Takeno2 has discussed a new type of nonlinear localized excitations (NLE) in one-dimensional discrete lattices.
Sergej Flach, Charles R. Willis
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Hamiltonian Mechanics of Discrete Particle Systems
1994In the previous chapter, we discussed briefly the fundamental nature of the symplectic structure of theories in optics in order to illustrate the underlying uniformity, physical consistency, and mathematical simplicity inherent to a symplectic mathematical formulation of the governing equations.
Antony N. Beris, Brian J. Edwards
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Continuous versus discrete free Hamiltonian systems
Journal of Physics A: Mathematical and Theoretical, 2013The Euclidean group contains two models of free Hamiltonian evolution: one has a continuous configuration space in which the wavefunctions obey the Helmholtz equation, and require two initial conditions: initial values and initial velocities; the other is based on a discrete position space where the wavefunctions obey a difference equation, and its ...
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