کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1897936 1044609 2008 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential
چکیده انگلیسی

We study analytically and numerically the stability of the standing waves for a nonlinear Schrödinger equation with a point defect and a power type nonlinearity. A major difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves. This 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 Hrad1(R) and unstable in H1(R)H1(R) under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup 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 nonradial 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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 237, Issue 8, 15 June 2008, Pages 1103–1128
نویسندگان
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