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Instability of bound states of a nonlinear Schrodinger equation with a Dirac potential

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84007

Title: Instability of bound states of a nonlinear Schrodinger equation with a Dirac potential
Authors: Le Coz,Stefan Browse this author
Fukuizumi, Reika Browse this author
Fibich, Gadi Browse this author
Ksherim, Baruch Browse this author
Sivan, Yonatan Browse this author
Issue Date: 2007
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 857
Start Page: 1
End Page: 43
Abstract: We study analytically and numerically the stability of the standing waves for a nonlinear Schr¨odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves, and it is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing wave solution is stable in H1 rad(R) and unstable in H1(R) under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blow-up in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a finite-width instability). In the non-radial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69666
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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