Klein-Gordon-Zakharov系统驻波解的不稳定性
Instability of the Standing Waves for the Klein-Gordon-Zakharov System
DOI: 10.12677/AAM.2025.147351, PDF,   
作者: 戴玉姣：长沙理工大学数学与统计学院, 湖南 长沙
关键词: Klein-Gordon-Zakharov 系统；驻波；轨道稳定；Virial 等式；Klein-Gordon-Zakharov System； Standing Waves； Orbital Stability； Virial Identity
摘要: 本文主要研究 Klein-Gordon-Zakharov(KGZ)系统驻波解在频率临界情况下的轨道稳定性。 为 了研究临界情况的稳定性，本文采用反证法，并结合强制性估计和调制理论，利用守恒量构造有 界的 virial 等式，最终证明了该 KGZ 系统驻波解在临界情况下是轨道不稳定的。
Abstract: In this paper, we focus on the orbital stability of standing wave solutions to the Klein- Gordon-Zakharov (KGZ) system in the critical frequency case. To investigate the stability under this critical condition, we employ a contradiction argument combined with coercivity and modulation theory. By utilizing conserved quantities, we construct a bounded virial-type identity, and ultimately establish the orbital instability of the standing wave solutions.
文章引用：戴玉姣. Klein-Gordon-Zakharov系统驻波解的不稳定性[J]. 应用数学进展, 2025, 14(7): 116-133. https://doi.org/10.12677/AAM.2025.147351

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