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Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Instability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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