Global existence of small classical solutions to nonlinear Schrödinger equations
Tohru Ozawa, Jian Zhai (2008)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “Nonlinear Schrödinger equation on four-dimensional compact manifolds”
Global existence of small classical solutions to nonlinear Schrödinger equations
Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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The Cauchy problem for the coupled Klein-Gordon-Schrödinger system
Changxing Miao, Youbin Zhu (2006)
Annales Polonici Mathematici
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We consider the Cauchy problem for a generalized Klein-Gordon-Schrödinger system with Yukawa coupling. We prove the existence of global weak solutions by the compactness method and, through a special choice of the admissible pairs to match two types of equations, we prove the uniqueness of those solutions by an approach similar to the method presented by J. Ginibre and G. Velo for the pure Klein-Gordon equation or pure Schrödinger equation. Though it is very simple in form, the method...
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.
Classical Solutions of Nonlinear Schrödinger Equations in Higher Dimensions.
Nakao Hayashi, Masayoshi Tsutsumi (1981)
Mathematische Zeitschrift
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The Cauchy problem for the nonlinear Schrödinger Equation in H1.
Thierry Cazenave, Fred B. Weissler (1988)
Manuscripta mathematica
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Classical Solutions of Nonlinear Schrödinger Equations.
Nakao Hayashi (1986)
Manuscripta mathematica
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Dunkl-Schrödinger Equations with and without Quadratic Potentials
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.
Positive solutions for nonlinear Schrödinger equations with deepening potential well
Zhengping Wang, Huan-Song Zhou (2009)
Journal of the European Mathematical Society
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On Solutions of the Initial Value Problem for the Nonlinear Schrödinger Equations in One Space Dimension.
N. Hayashi, K. Nakamitsu, M. Tsutsumi (1986)
Mathematische Zeitschrift
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Numerical study of self-focusing solutions to the Schrödinger-Debye system
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.