Small Amplitude Traveling Waves in the Full-Dispersion Whitham Equation

In this article, we provide an alternative way to construct small amplitude traveling waves for general Whitham type equations, in both periodic and whole line contexts. More specifically, Fourier analysis techniques allow us to reformulate the problem to the study of waves that are small and regula...

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Bibliographic Details
Published in:Journal of dynamics and differential equations 2020-03, Vol.32 (1), p.85-99
Main Authors: Stefanov, Atanas, Wright, J. Douglas
Format: Article
Language:English
Subjects:
Amplitudes
Applications of Mathematics
Fourier analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Traveling waves
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Summary:In this article, we provide an alternative way to construct small amplitude traveling waves for general Whitham type equations, in both periodic and whole line contexts. More specifically, Fourier analysis techniques allow us to reformulate the problem to the study of waves that are small and regular perturbations of well-understood ODE’s. In addition, rigorous spectral stability of these waves is established.
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-018-9713-8