标题:Strong instability of standing waves for a fourth-order nonlinear Schrödinger equation with the mixed dispersions
作者:Feng B.; Liu J.; Niu H.; Zhang B.
作者机构:[Feng, B] Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China;[ Liu, J] School of Mathematics and Information Science, Nort 更多
通讯作者:Zhang, B(zhangbinlin2012@163.com)
通讯作者地址:[Zhang, B] College of Mathematics and Systems Sciences, Shandong University of Science and TechnologyChina;
来源:Nonlinear Analysis, Theory, Methods and Applications
出版年:2020
卷:196
DOI:10.1016/j.na.2020.111791
关键词:Bi-harmonic nonlinear Schrödinger equation; Ground state; Strong instability
摘要:In this paper, we consider the strong instability of standing waves for a fourth-order nonlinear Schrödinger equation with the mixed dispersions iψt−γΔ2ψ+μΔψ+|ψ|pψ=0,(t,x)∈[0,T∗)×RN,where γ>0 and μ<0. This equation arises in describing the propagation of intense laser beams in a bulk medium with Kerr nonlinearity. We firstly obtain the variational characterization of ground state solutions by using the profile decomposition theory in H2. Then, we deduce that if ∂λ 2Sω(uλ)|λ=1≤0, the ground state standing wave eiωtu is strongly unstable by blow-up, where uλ(x)=λN2u(λx) and Sω is the action. This result is a complement to the result of Bonheure et al. (2019), where the strong instability of standing waves has been studied in the case μ>0. © 2020 Elsevier Ltd
收录类别:SCOPUS
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85079286116&doi=10.1016%2fj.na.2020.111791&partnerID=40&md5=360406b3bf32a1fc08d9a10a0d7422bd
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