Displaying similar documents to “A Survey on Systems of Nonlinear Schrödinger Equations”

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.

Bilinear virial identities and applications

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.

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.