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Multi-symplectic integration of coupled non-linear Schrödinger system with soliton solutions. (English) Zbl 1165.65084
Summary: Systems of coupled nonlinear 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.

MSC:
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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