Symplectic and multi-symplectic methods for coupled nonlinear Schrodinger equations with periodic solutions

Date

2007-10-01

Author

Aydin, A.
Karasoezen, B.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

182
views

0
downloads

We consider for the integration of coupled nonlinear Schrodinger equations with periodic plane wave solutions a splitting method from the class of symplectic integrators and the multi-symplectic six-point scheme which is equivalent to the Preissman scheme. The numerical experiments show that both methods preserve very well the mass, energy and momentum in long-time evolution. The local errors in the energy are computed according to the discretizations in time and space for both methods. Due to its local nature, the multi-symplectic six-point scheme preserves the local invariants more accurately than the symplectic splitting method, but the global errors for conservation laws are almost the same.

Subject Keywords

Hardware and Architecture, General Physics and Astronomy

URI

https://hdl.handle.net/11511/65126

Journal

COMPUTER PHYSICS COMMUNICATIONS

DOI

https://doi.org/10.1016/j.cpc.2007.05.010

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Discrete symmetries and nonlocal reductions GÜRSES, METİN; Pekcan, Asli; Zheltukhın, Kostyantyn (Elsevier BV, 2020-01-31) We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
Discretization error due to the identity operator in surface integral equations Ergül, Özgür Salih (Elsevier BV, 2009-10-01) We consider the accuracy of surface integral equations for the solution of scattering and radiation problems in electromagnetics. In numerical solutions, second-kind integral equations involving well-tested identity operators are preferable for efficiency, because they produce diagonally-dominant matrix equations that can be solved easily with iterative methods. However, the existence of the well-tested identity operators leads to inaccurate results, especially when the equations are discretized with low-or...
Anti-de Sitter-Wave Solutions of Higher Derivative Theories GÜRSES, METİN; Hervik, Sigbjorn; Sisman, Tahsin Cagri; Tekin, Bayram (American Physical Society (APS), 2013-09-05) We show that the recently found anti-de Sitter (AdS)-plane and AdS-spherical wave solutions of quadratic curvature gravity also solve the most general higher derivative theory in D dimensions. More generally, we show that the field equations of such theories reduce to an equation linear in the Ricci tensor for Kerr-Schild spacetimes having type-N Weyl and type-N traceless Ricci tensors.
Approximate l-state solutions of the D-dimensional Schrodinger equation for Manning-Rosen potential IKHDAİR, SAMEER; Sever, Ramazan (Wiley, 2008-11-01) The Schrodinger equation in D-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The Nikiforov-Uvarov (NU) method is used in the calculations. We present numerical calculations of energy eigenvalues to two- and four-dimensional systems for arbitrary quantum numbers n and 1, with three different values of the potential parameter alpha. It is shown that because of the interdimensional degeneracy o...
Approximate solution to the time-dependent Kratzer plus screened Coulomb potential in the Feinberg-Horodecki equation Farout, Mahmoud; Sever, Ramazan; Ikhdair, Sameer M. (IOP Publishing, 2020-06-01) We obtain the quantized momentum eigenvalues P-n together with space-like coherent eigenstates for the space-like counterpart of the Schrodinger equation, the Feinberg-Horodecki equation, with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.

Citation Formats

A. Aydin and B. Karasoezen, “Symplectic and multi-symplectic methods for coupled nonlinear Schrodinger equations with periodic solutions,” COMPUTER PHYSICS COMMUNICATIONS, pp. 566–583, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65126.