کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6417169 1338533 2015 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the wave length of smooth periodic traveling waves of the Camassa-Holm equation
ترجمه فارسی عنوان
در طول موج امواج حرکتی صاف دوره ای از معادله کمسا-هولم
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

This paper is concerned with the wave length λ of smooth periodic traveling wave solutions of the Camassa-Holm equation. The set of these solutions can be parametrized using the wave height a (or “peak-to-peak amplitude”). Our main result establishes monotonicity properties of the map a⟼λ(a), i.e., the wave length as a function of the wave height. We obtain the explicit bifurcation values, in terms of the parameters associated with the equation, which distinguish between the two possible qualitative behaviors of λ(a), namely monotonicity and unimodality. The key point is to relate λ(a) to the period function of a planar differential system with a quadratic-like first integral, and to apply a criterion which bounds the number of critical periods for this type of systems.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 259, Issue 6, 15 September 2015, Pages 2317-2332
نویسندگان
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