周期Lugiato-Lefever波的前向调制阻尼估计和非定域稳定性
Forward-modulated damping estimates and nonlocalized stability of periodic Lugiato-Lefever wave
摘要：
在最近一个有趣的分析中，Haragus-Johnson-Perkins-de Rijk在Lugiato-Lefever方程（LLE）的稳定周期解的局部扰动下显示了调制稳定性，在此过程中指出了在调制扰动变量上获得标准的“非线性阻尼估计”以控制解的正则性的困难。在这里，我们指出，在标准的“逆调制”阻尼估计的地方，人们可以选择进行阻尼估计的“正向调制”扰动，注意到，规范的正向和逆调制变量是等效模吸收误差，从而恢复经典的论点结构的约翰逊-诺布尔-罗德里格斯-宗布伦抛物系统。这种观察似乎在具有微妙规律性的情况下普遍使用。应用于（LLE）的背景下，它给出了更强的结果的稳定性和渐近行为的非局部扰动。
英文摘要：
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.
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