Classical Solutions of Nonlinear Schrödinger Equations in Higher Dimensions.
Nakao Hayashi, Masayoshi Tsutsumi (1981)
Mathematische Zeitschrift
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Nakao Hayashi, Masayoshi Tsutsumi (1981)
Mathematische Zeitschrift
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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.
Zhengping Wang, Huan-Song Zhou (2009)
Journal of the European Mathematical Society
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Nakao Hayashi (1986)
Manuscripta mathematica
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Nakao Hayashi, Tohru Ozawa (1988/89)
Mathematische Zeitschrift
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Wolf von Wahl, Hartmut Pecher (1979)
Manuscripta mathematica
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Arne Jensen (1986)
Mathematische Zeitschrift
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Thierry Cazenave, Fred B. Weissler (1988)
Manuscripta mathematica
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Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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M. Hoffmann-Ostenhof (1988)
Mathematische Zeitschrift
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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.