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Numerical solution to coupled nonlinear Schrödinger equations on unbounded domains. (English) Zbl 1197.65162
Summary: The numerical simulation of coupled nonlinear Schrödinger equations on unbounded domains is considered. By using the operator splitting technique, the original problem is decomposed into linear and nonlinear subproblems in a small time step. The linear subproblem turns out to be two decoupled linear Schrödinger equations on unbounded domains, where artificial boundaries are introduced to truncate the unbounded physical domains into finite ones. Local absorbing boundary conditions are imposed on the artificial boundaries. On the other hand, the coupled nonlinear subproblem is a system of ordinary differential equations, which can be solved exactly. To demonstrate the effectiveness of our method, some comparisons in terms of accuracy and computational cost are made between the perfectly matched layer approach and our method in numerical examples.
MSC:
65M70Spectral, collocation and related methods (IVP of PDE)
35Q55NLS-like (nonlinear Schrödinger) equations
35Q51Soliton-like equations
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