Instability of standing waves for inhomogeneous Hartree equations

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• 作者：Qing Guo^a ; ^{guoqing@amss.ac.cn" class="auth_mail" title="E-mail the corresponding author} ; Yiming Su^b ; ^{yimingsu@amss.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hartree equations ; Instability ; Standing-wave solutions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：437
• 期：2
• 页码：1159-1175
• 全文大小：413 K

文摘

We are concerned with the instability of standing-wave solutions e^iωtφ_ω(x)$e^{i\omega t}{\phi }_{\omega }(x)$ to the Hartree equation iu_t+Δu+gu(|⋅|^−γ⁎(g|u|²))=0$i{u}_t+\mathrm{\Delta }u+gu(|\cdot {|}^{-\gamma }⁎(g|u{|}^2))=0$ for some suitable g(x)$g(x)$, where φ_ω${\phi }_{\omega }$ is a ground state solution. The instability of standing-wave solutions reveals a balance between ω and γ.