Energy preserving methods for lattice equations

Integral preserving methods, like the averaged vector field, discrete gradient and trapezoidal methods are to Poisson systems. Numerical experiments on the Volterra equations and integrable discretization of the nonlinear Schrodinger equation are presented.


Energy preserving integration of bi-Hamiltonian partial differential equations
Karasözen, Bülent (2013-12-01)
The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the long term preservation of the Hamiltonians and Casimir integrals, which is essential in simulating waves and solitons. Dispersive properties of the AVF integrator are investigated for the linearized equations to ex...
Hilbert functions of gorenstein monomial curves
Topaloğlu Mete, Pınar; Arslan, Sefa Feza; Department of Mathematics (2005)
The aim of this thesis is to study the Hilbert function of a one-dimensional Gorenstein local ring of embedding dimension four in the case of monomial curves. We show that the Hilbert function is non-decreasing for some families of Gorenstein monomial curves in affine 4-space. In order to prove this result, under some arithmetic assumptions on generators of the defining ideal, we determine the minimal generators of their tangent cones by using the standard basis and check the Cohen-Macaulayness of them. Lat...
Moving mesh discontinuous Galerkin methods for PDEs with traveling waves
UZUNCA, MURAT; Karasözen, Bülent; Kucukseyhan, T. (2017-01-01)
In this paper, a moving mesh discontinuous Galerkin (dG) method is developed for nonlinear partial differential equations (PDEs) with traveling wave solutions. The moving mesh strategy for one dimensional PDEs is based on the rezoning approach which decouples the solution of the PDE from the moving mesh equation. We show that the dG moving mesh method is able to resolve sharp wave fronts and wave speeds accurately for the optimal, arc-length and curvature monitor functions. Numerical results reveal the effi...
Average Vector Field Splitting Method for Nonlinear Schrodinger Equation
Akkoyunlu, Canan; Karasözen, Bülent (2012-05-02)
The energy preserving average vector field integrator is applied to one and two dimensional Schrodinger equations with symmetric split-step method. The numerical results confirm the long-term preservation of the Hamiltonians, which is essential in simulating periodic waves.
ERIS, A; GURSES, M; Karasu, Atalay (AIP Publishing, 1984-01-01)
We formulate stationary axially symmetric (SAS) Einstein–Maxwell fields in the framework of harmonic mappings of Riemannian manifolds and show that the configuration space of the fields is a symmetric space. This result enables us to embed the configuration space into an eight‐dimensional flat manifold and formulate SAS Einstein–Maxwell fields as a σ‐model. We then give, in a coordinate free way, a Belinskii–Zakharov type of an inverse scattering transform technique for the field equations supplemented by a...
Citation Formats
Ö. Erdem and B. Karasözen, “Energy preserving methods for lattice equations,” 2010, vol. 1309, Accessed: 00, 2020. [Online]. Available: