A Survey on Systems of Nonlinear Schrödinger Equations
Antonio Ambrosetti (2008)
Bollettino dell'Unione Matematica Italiana
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We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.
Antonio Ambrosetti (2008)
Bollettino dell'Unione Matematica Italiana
Similarity:
We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.
Zhengping Wang, Huan-Song Zhou (2009)
Journal of the European Mathematical Society
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Rémi Carles, Bijan Mohammadi (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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We study numerically the semiclassical limit for the nonlinear Schrödinger equation thanks to a modification of the Madelung transform due to Grenier. This approach allows for the presence of vacuum. Even if the mesh size and the time step do not depend on the Planck constant, we recover the position and current densities in the semiclassical limit, with a numerical rate of convergence in accordance with the theoretical results, before shocks appear in the limiting Euler equation....
Rémi Carles, Bijan Mohammadi (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We study numerically the semiclassical limit for the nonlinear Schrödinger equation thanks to a modification of the Madelung transform due to Grenier. This approach allows for the presence of vacuum. Even if the mesh size and the time step do not depend on the Planck constant, we recover the position and current densities in the semiclassical limit, with a numerical rate of convergence in accordance with the theoretical results, before shocks appear in the limiting Euler equation....
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