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
通讯作者地址：[Zhang, B] College of Mathematics and Systems Sciences, Shandong University of Science and TechnologyChina;
来源：Nonlinear Analysis, Theory, Methods and Applications
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