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Article Citation - WoS: 13Multi-symplectic integration of coupled non-linear Schrodinger system with soliton solutions(Taylor & Francis Ltd, 2009) Aydin, Ayhan; Karasoezen, BuelentSystems 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.Article Citation - WoS: 39Citation - Scopus: 44Symplectic and Multi-Symplectic Methods for Coupled Nonlinear Schrodinger Equations With Periodic Solutions(Elsevier, 2007) Aydin, A.; Karasoezen, B.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. (C) 2007 Elsevier B.V. All rights reserved.
