论文标题
$ ϕ^4 $ model的周期性波解决方案的轨道稳定性和不稳定性
Orbital stability and instability of periodic wave solutions for the $ϕ^4$-model
论文作者
论文摘要
在这项工作中，我们发现了经典$ ϕ^4 $模型的明确周期性波解决方案，并研究了它们在能量空间中相应的轨道稳定性/不稳定。特别是，对于此模型，我们发现至少四个不同的在空间周期波解的分支，可以用雅各比椭圆函数编写。这些分支中的两个对应于超亮性波，第三个对应于亚延伸波，其余一个对应于固定的复合物值波。在这项工作中，我们证明了轨道不稳定性，实现的，灯 - 灯泡的下波浪和固定的复合物值波。此外，我们证明，在一些其他假设下，零速亚延迟病例是稳定的。后一种情况（从某种意义上说）与经典的纠结解决方案有关。
In this work we find explicit periodic wave solutions for the classical $ϕ^4$-model, and study their corresponding orbital stability/instability in the energy space. In particular, for this model we find at least four different branches of spatially-periodic wave solutions, which can be written in terms of Jacobi elliptic functions. Two of these branches correspond to superluminal waves, a third-one corresponding to a sub-luminal wave and the remaining one corresponding to a stationary complex-valued wave. In this work we prove the orbital instability of both, real-valued sub-luminal traveling waves and stationary complex-valued waves. Furthermore, we prove that under some additional hypothesis the zero-speed sub-luminal case is stable. This latter case is related (in some sense) to the classical Kink solution.
