کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8896694 | 1630596 | 2018 | 37 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Linear asymptotic stability and modulation behavior near periodic waves of the Korteweg-de Vries equation
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Linear asymptotic stability and modulation behavior near periodic waves of the Korteweg-de Vries equation Linear asymptotic stability and modulation behavior near periodic waves of the Korteweg-de Vries equation](/preview/png/8896694.png)
چکیده انگلیسی
We provide a detailed study of the dynamics obtained by linearizing the Korteweg-de Vries equation about one of its periodic traveling waves, a cnoidal wave. In a suitable sense, linearly analogous to space-modulated stability [15], we prove global-in-time bounded stability in any Sobolev space, and asymptotic stability of dispersive type. Furthermore, we provide both a leading-order description of the dynamics in terms of slow modulation of local parameters and asymptotic modulation systems and effective initial data for the evolution of those parameters. This requires a global-in-time study of the dynamics generated by a non normal operator with non constant coefficients. On the road we also prove estimates on oscillatory integrals particularly suitable to derive large-time asymptotic systems that could be of some general interest.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 274, Issue 9, 1 May 2018, Pages 2553-2605
Journal: Journal of Functional Analysis - Volume 274, Issue 9, 1 May 2018, Pages 2553-2605
نویسندگان
L. Miguel Rodrigues,