论文标题
一些克莱因 - 戈登类型方程的奇数周期波：存在与稳定性
Odd Periodic Waves for some Klein-Gordon Type Equations: Existence and Stability
论文作者
论文摘要
在本文中，我们建立了与klein-gordon类型方程相关的奇数周期性波的存在和稳定性，其中包括众所周知的$ ϕ^4 $和$ ϕ^6 $模型。周期性波的存在是通过使用ode的一般平面理论来确定的。使用时期图的单调性与标准浮雕理论的改进相结合，建立了相应的线性化操作员的光谱分析。使用时期图的单调性证明了能量空间奇数扇区中的轨道稳定性。使用\ cite {grillakis1}中的抽象方法提出了$ ϕ^4 $和$ ϕ^6 $模型的显式解决方案的轨道不稳定。
In this paper, we establish the existence and stability properties of odd periodic waves related to the Klein-Gordon type equations, which include the well known $ϕ^4$ and $ϕ^6$ models. Existence of periodic waves is determined by using a general planar theory of ODE. The spectral analysis for the corresponding linearized operator is established using the monotonicity of the period map combined with an improvement of the standard Floquet theory. Orbital stability in the odd sector of the energy space is proved using exclusively the monotonicity of the period map. The orbital instability of explicit solutions for the $ϕ^4$ and $ϕ^6$ models is presented using the abstract approach in \cite{grillakis1}.
