### 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.

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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.

Christophe Besse, Brigitte Bidégaray (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.

B.V. Limaye, R.P. Kulkarni (1983)

Numerische Mathematik

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Zhengping Wang, Huan-Song Zhou (2009)

Journal of the European Mathematical Society

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Ciegis, R., Pakeniene, V. (2001)

Computational Methods in Applied Mathematics

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N. Hayashi, K. Nakamitsu, M. Tsutsumi (1986)

Mathematische Zeitschrift

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M. Marion, R. Temam (1990)

Numerische Mathematik

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Nakao Hayashi (1986)

Manuscripta mathematica

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Wolf von Wahl, Hartmut Pecher (1979)

Manuscripta mathematica

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Nakao Hayashi, Masayoshi Tsutsumi (1981)

Mathematische Zeitschrift

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Eugenio Montefusco, Benedetta Pellacci, Marco Squassina (2008)

Journal of the European Mathematical Society

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We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.

Thierry Cazenave, Fred B. Weissler (1988)

Manuscripta mathematica

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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

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