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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Zhengping Wang, Huan-Song Zhou (2009)
Journal of the European Mathematical Society
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N. Hayashi, K. Nakamitsu, M. Tsutsumi (1986)
Mathematische Zeitschrift
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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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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.
Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Thierry Cazenave, Fred B. Weissler (1988)
Manuscripta mathematica
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Laurent Thomann (2008)
Bulletin de la Société Mathématique de France
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In this paper we are interested in constructing WKB approximations for the nonlinear cubic Schrödinger equation on a Riemannian surface which has a stable geodesic. These approximate solutions will lead to some instability properties of the equation.
Fabrice Planchon, Luis Vega (2009)
Annales scientifiques de l'École Normale Supérieure
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We prove bilinear virial identities for the nonlinear Schrödinger equation, which are extensions of the Morawetz interaction inequalities. We recover and extend known bilinear improvements to Strichartz inequalities and provide applications to various nonlinear problems, most notably on domains with boundaries.
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.
Merle, Frank (1998)
Documenta Mathematica
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