کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1899726 1534061 2010 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
On the modulation equations and stability of periodic generalized Korteweg-de Vries waves via Bloch decompositions
چکیده انگلیسی
In this paper, we consider the relation between Evans-function-based approaches to the stability of periodic travelling waves and other theories based on long-wavelength asymptotics together with Bloch wave expansions. In previous work it was shown by rigorous Evans function calculations that the formal slow modulation approximation resulting in the linearized Whitham averaged system accurately describes the spectral stability to long-wavelength perturbations. To clarify the connection between Bloch-wave-based expansions and Evans-function-based approaches, we reproduce this result without reference to the Evans function by using direct Bloch expansion methods and spectral perturbation analysis. One of the novelties of this approach is that we are able to calculate the relevant Bloch waves explicitly for arbitrary finite-amplitude solutions. Furthermore, this approach has the advantage of being applicable in the more general multi-periodic setting where no conveniently computable Evans function has yet been devised.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 239, Issues 23–24, 1 November 2010, Pages 2057-2065
نویسندگان
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