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Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities
Title: | Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities |
Authors: | DE BOUARD, Anne Browse this author | FUKUIZUMI, Reika Browse this author |
Issue Date: | 2004 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 700 |
Start Page: | 1 |
End Page: | 18 |
Abstract: | The effect of inhomogenity of nonlinear medium is discussed concerning the stability of standing waves eiωtφω(x) for a nonlinear Schrödinger equation with an inhomogeneous nonlinearity V (x)|u|p-1u, where V(x) is proportional to the electron density. Here, ω > 0 and φω(x) is a ground state of the stationary problem. When V(x) behaves like |x|-b at in nity, where 0 < b < 2, we show that eiωtφω(x) is stable for p < 1 + (4 - 2b)=n and sufficiently small ω > 0. The main point of this paper is to analyze the linearized operator at standing wave solution for the case of V (x) = |x|-b. Then, this analysis yields a stability result for the case of more general, inhomogeneous V (x) by a certain perturbation method. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69505 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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