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Local discontinuous Galerkin methods for nonlinear Schrödinger equations. (English) Zbl 1072.65130
Summary: We develop a local discontinuous Galerkin method to solve the generalized nonlinear Schrödinger equation and the coupled nonlinear Schrödinger equation. $$L^2$$ stability of the schemes is obtained for both of these nonlinear equations. Numerical examples are shown to demonstrate the accuracy and capability of these methods.

##### MSC:
 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35Q55 NLS equations (nonlinear Schrödinger equations)
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