论文标题
周期性Lugiato-Lefever波的正向调节阻尼估计和非定位的稳定性
Forward-modulated damping estimates and nonlocalized stability of periodic Lugiato-Lefever wave
论文作者
论文摘要
在最近的一项有趣的分析中，Haragus-Johnson-Perkins-De Rijk在稳定的Lugiato-Lefever方程（LLE）稳定周期溶液的局部扰动下显示了模量稳定性，在该过程中指出了难以获得标准的“非线性阻尼估计”，“在调节扰动上的均匀扰动估计值中”。 Here, we point out that in place of standard "inverse-modulated" damping estimates, one can alternatively carry out a damping estimate on the "forward-modulated" perturbation, noting that norms of forward- and inverse-modulated variables are equivalent modulo absorbable errors, thus recovering the classical argument structure of Johnson-Noble-Rodrigues-Zumbrun for parabolic systems.在微妙的规律性情况下，这种观察似乎是一般使用。 在（LLE）的背景下，它在非定位扰动方面给出了稳定性和渐近行为的更强结果。
In an interesting recent analysis, Haragus-Johnson-Perkins-de Rijk have shown modulational stability under localized perturbations of steady periodic solutions of the Lugiato-Lefever equation (LLE), in the process pointing out a difficulty in obtaining standard "nonlinear damping estimates" on modulated perturbation variables to control regularity of solutions. Here, we point out that in place of standard "inverse-modulated" damping estimates, one can alternatively carry out a damping estimate on the "forward-modulated" perturbation, noting that norms of forward- and inverse-modulated variables are equivalent modulo absorbable errors, thus recovering the classical argument structure of Johnson-Noble-Rodrigues-Zumbrun for parabolic systems. This observation seems of general use in situations of delicate regularity. Applied in the context of (LLE) it gives the stronger result of stability and asymptotic behavior with respect to nonlocalized perturbations.
