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.
Displaying similar documents to “Positive solutions for nonlinear Schrödinger equations with deepening potential well”
A Survey on Systems of Nonlinear Schrödinger Equations
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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Classical Solutions of Nonlinear Schrödinger Equations.
Nakao Hayashi (1986)
Manuscripta mathematica
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Time Dependent Nonlinear Schrödinger Equations.
Wolf von Wahl, Hartmut Pecher (1979)
Manuscripta mathematica
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Semiclassical states for weakly coupled nonlinear Schrödinger systems
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.
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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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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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.
Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations.
Merle, Frank (1998)
Documenta Mathematica
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The WKB method and geometric instability for nonlinear Schrödinger equations on surfaces
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.
Hardy's uncertainty principle, convexity and Schrödinger evolutions
Luis Escauriaza, Carlos E. Kenig, G. Ponce, Luis Vega (2008)
Journal of the European Mathematical Society
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We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schrödinger evolutions. As a consequence we obtain some uniqueness results that generalize (a weak form of) Hardy’s version of the uncertainty principle. We also obtain corresponding results for heat evolutions.
A multiplicity result for the Schrodinger-Maxwell equations with negative potential
Giuseppe Maria Coclite (2002)
Annales Polonici Mathematici
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We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.