Multi-symplectic integration of coupled non-linear Schrodinger system with soliton solutions

Date

2009-01-01

Author

AYDIN, AYHAN
Karasözen, Bülent

Metadata

Show full item record

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

Item Usage Stats

297
views

0
downloads

Systems of coupled non-linear Schrodinger equations with soliton solutions are integrated using the six-point scheme which is equivalent to the multi-symplectic Preissman scheme. The numerical dispersion relations are studied for the linearized equation. Numerical results for elastic and inelastic soliton collisions are presented. Numerical experiments confirm the excellent conservation of energy, momentum and norm in long-term computations and their relations to the qualitative behaviour of the soliton solutions.

Subject Keywords

Coupled nonlinear Schrodinger equation, Solitons, Dispersion, Multi-symplectic methods

URI

https://hdl.handle.net/11511/32609

Journal

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

DOI

https://doi.org/10.1080/00207160701713615

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Unpredictable solutions of linear differential and discrete equations Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (2019-01-01) The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincare chaos. Simulations illustrating the chaos are provided.
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems Bozkaya, Canan (2005-03-18) The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Backward stochastic differential equations and Feynman-Kac formula in the presence of jump processes İncegül Yücetürk, Cansu; Yolcu Okur, Yeliz; Hayfavi, Azize; Department of Financial Mathematics (2013) Backward Stochastic Differential Equations (BSDEs) appear as a new class of stochastic differential equations, with a given value at the terminal time T. The application area of the BSDEs is conceptually wide which is known only for forty years. In financial mathematics, El Karoui, Peng and Quenez have a fundamental and significant article called “Backward Stochastic Differential Equations in Finance” (1997) which is taken as a groundwork for this thesis. In this thesis we follow the following steps: Firstl...
Lobatto IIIA-IIIB discretization of the strongly coupled nonlinear Schrodinger equation AYDIN, AYHAN; Karasözen, Bülent (2011-06-15) In this paper, we construct a second order semi-explicit multi-symplectic integrator for the strongly coupled nonlinear Schrodinger equation based on the two-stage Lobatto IIIA-IIIB partitioned Runge-Kutta method. Numerical results for different solitary wave solutions including elastic and inelastic collisions, fusion of two solitons and with periodic solutions confirm the excellent long time behavior of the multi-symplectic integrator by preserving global energy, momentum and mass.
NUMERICAL ANALYSIS AND TESTING OF A FULLY DISCRETE, DECOUPLED PENALTY-PROJECTION ALGORITHM FOR MHD IN ELSASSER VARIABLE AKBAŞ, MİNE; Kaya Merdan, Songül; MOHEBUJJAMAN, Muhammed; rebholz, leo (2016-01-01) We consider a fully discrete, efficient algorithm for magnetohydrodynamic (MHD) flow that is based on the Elsasser variable formulation and a timestepping scheme that decouples the MHD system but still provides unconditional stability with respect to the timestep. We prove stability and optimal convergence of the scheme, and also connect the scheme to one based on handling each decoupled system with a penalty-projection method. Numerical experiments are given which verify all predicted convergence rates of ...

Citation Formats

A. AYDIN and B. Karasözen, “Multi-symplectic integration of coupled non-linear Schrodinger system with soliton solutions,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, pp. 864–882, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32609.