Resonant averaging for weakly nonlinear stochastic Schrödinger equations
Sergei B. Kuksin (2013-2014)
Séminaire Laurent Schwartz — EDP et applications
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Sergei B. Kuksin (2013-2014)
Séminaire Laurent Schwartz — EDP et applications
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Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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.
Mejjaoli, Hatem (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10. The purpose of this paper is to study the dispersive properties of the solutions of the Dunkl-Schrödinger equation and their perturbations with potential. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems.
N. Hayashi, K. Nakamitsu, M. Tsutsumi (1986)
Mathematische Zeitschrift
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