Strong Instability of Standing Waves for the Nonlinear Klein-Gordon Equation and the Klein-Gordon-Zakharov System
Strong Instability of Standing Waves for the Nonlinear Klein-Gordon Equation and the Klein-Gordon-Zakharov System
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DOI：
10.1137/050643015
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发表时间：
2007-03
期刊：
影响因子：
--
通讯作者：
Masahito Ohta;G. Todorova
中科院分区：
文献类型：
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作者：
Masahito Ohta;G. Todorova
对于非线性Klein-Gordon方程，基态驻波$e^{i\omega t}\phi_{\omega}(x)$的轨道不稳定性在超临界情况下在所有频率ω域中已知，在亚临界情况下在严格小于临界频率$\omega_c$的频率域中已知。我们证明了整个区域的基态驻波的强不稳定性。对于频率等于临界频率$\omega_c$的情况，我们证明了所有径向对称驻波$e^{i\omega_c t}\varphi(x)$的强不稳定性。我们证明了Klein-Gordon-Zakharov系统类似的强不稳定性结果。
The orbital instability of ground state standing waves $e^{i\omega t}\phi_{\omega}(x)$ for the nonlinear Klein–Gordon equation has been known in the domain of all frequencies ω for the supercritical case and for frequencies strictly less than a critical frequency $\omega_c$ in the subcritical case. We prove the strong instability of ground state standing waves for the entire domain above. For the case when the frequency is equal to the critical frequency $\omega_c$ we prove strong instability for all radially symmetric standing waves $e^{i\omega_c t}\varphi(x)$. We prove similar strong instability results for the Klein–Gordon–Zakharov system.