High Frequency Perturbation of Cnoidal Waves in KdV

The KdV equation with periodic boundary conditions is considered. The interaction of a periodic solitary wave (cnoidal wave) with high frequency radiation of finite energy ($L^2$ norm) is studied. It is proved that the interaction of a low frequency component (cnoidal wave) and high frequency radiat...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2012-01, Vol.44 (6), p.4147-4164
Main Authors: Erdoğan, M. B., Tzirakis, N., Zharnitsky, V.
Format: Article
Language:English
Subjects:
Boundary conditions
Energy
Radiation
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Summary:The KdV equation with periodic boundary conditions is considered. The interaction of a periodic solitary wave (cnoidal wave) with high frequency radiation of finite energy ($L^2$ norm) is studied. It is proved that the interaction of a low frequency component (cnoidal wave) and high frequency radiation is weak for finite time in the following sense: the radiation approximately satisfies the Airy equation. [PUBLICATION ABSTRACT]
ISSN:0036-1410
1095-7154
DOI:10.1137/120868220