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

Karasözen, Bülent
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.


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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.
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: