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 “Bilinear virial identities and applications”
A Survey on Systems of Nonlinear Schrödinger Equations
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On Solutions of the Initial Value Problem for the Nonlinear Schrödinger Equations in One Space Dimension.
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Classical Solutions of Nonlinear Schrödinger Equations in Higher Dimensions.
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Classical Solutions of Nonlinear Schrödinger Equations.
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Jean Bourgain, W. Wang (1997)
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Time Dependent Nonlinear Schrödinger Equations.
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The Cauchy problem for the nonlinear Schrödinger Equation in H1.
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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.
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.
Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions
Filip Ficek (2023)
Archivum Mathematicum
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Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials. ...
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.