Related papers: Mid-point embedding of Hamiltonian systems and var…
We express discrete Painlev\'e equations as discrete Hamiltonian systems. The discrete Hamiltonian systems here mean the canonical transformations defined by generating functions. Our construction relies on the classification of the…
We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories…
In this paper, we introduce two types of variational integrators, one originating from the discrete Hamilton's principle while the other from Galerkin variational approach. It turns out that these variational integrators are equivalent to…
Compatible discretizations, such as finite element exterior calculus, provide a discretization framework that respect the cohomological structure of the de Rham complex, which can be used to systematically construct stable mixed finite…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…
Recently, a new family of integrators (Hamiltonian Boundary ValueMethods) has been introduced, which is able to precisely conserve the energy function of polynomial Hamiltonian systems and to provide a practical conservation of the energy…
We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the…
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…
A discrete theory for implicit nonholonomic Lagrangian systems undergoing elastic collisions is developed. It is based on the discrete Lagrange-d'Alembert-Pontryagin variational principle and the dynamical equations thus obtained are the…
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the…
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved…
We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…
In this paper we study local Hamiltonian operators for multi-component evolutionary differential-difference equations. We address two main problems: the first one is the classification of low order operators for the two-component case. On…
A variational formulation for accelerated optimization on normed vector spaces was recently introduced in Wibisono et al., and later generalized to the Riemannian manifold setting in Duruisseaux and Leok. This variational framework was…
The superintegrability of two-dimensional Hamiltonians with a position dependent mass (pdm) is studied (the kinetic term contains a factor $m$ that depends of the radial coordinate). First, the properties of Killing vectors are studied and…