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Instability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83849

Title: Instability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities
Authors: FUKUIZUMI, Reika Browse this author
OHTA, Masahito Browse this author
Issue Date: 2004
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 698
Start Page: 1
End Page: 12
Abstract: We study the instability of standing waves eiωtφω(x) for a nonlinear Schr odinger equation with an inhomogeneous nonlinearity V (x)jujp-1u. 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 unstable for p > 1 + (4 - 2b)=n and sufficiently small ω > 0. Due to the inhomogeneous medium, the unstable effect occurs in the region 1 + (4 - 2b)=n < p < 1 + 4=n which is the stable region in the case where V (x) 1.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69503
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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