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Article Lobatto Iiia–iiib Discretization of the Strongly Coupled Nonlinear Schrödinger Equation(Journal of Computational and Applied Mathematics, 2009) Aydın, Ayhan; Karasözen, BülentIn this paper, we construct a second order semi-explicit multi-symplectic integrator for the strongly coupled nonlinear Schrödinger 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.Article Symplectic and multi-symplectic methods for coupled nonlinear Schrödinger equations with periodic solutions(Computer Physics Communications, 2007) Aydın, Ayhan; Karasözen, BülentWe consider for the integration of coupled nonlinear Schrödinger 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.Article Multi-Symplectic Integration of Coupled Non-Linear Schrödinger System With Soliton Solutions(International Journal of Computer Mathematics, 2009) Aydın, Ayhan; Aydın, Ayhan; Karasözen, Bülent; Aydın, Ayhan; Mathematics; MathematicsSystems of coupled non-linear Schrödinger 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.
