Instability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities

FUKUIZUMI, Reika; OHTA, Masahito

Hokkaido University Preprint Series in Mathematics, 2004, 698, 1-12

Permalink : https://doi.org/10.14943/83849

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アクセス権	open access
DOI	https://doi.org/10.14943/83849
URI	https://hdl.handle.net/2115/69503
タイトル	Instability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities
著者	著者名 FUKUIZUMI, Reika
著者	著者名 OHTA, Masahito
言語	英語
発行日	2004
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	698
ページ	1-12
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record