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Terminal Damping of a Solitary Wave Due to Radiation in Rotational Systems
Author(s) -
Grimshaw R. H. J.,
He J.M.,
Ostrovsky L. A.
Publication year - 1998
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00090
Subject(s) - rotation (mathematics) , physics , amplitude , phase velocity , synchronism , classical mechanics , action (physics) , dispersion (optics) , angular velocity , mathematical analysis , quantum electrodynamics , mathematics , optics , quantum mechanics , geometry , voltage
The evolution of a solitary wave under the action of rotation is considered within the framework of the rotation‐modified Korteweg–de Vries equation. Using an asymptotic procedure, the solitary wave is shown to be damped due to radiation of a dispersive wave train propagating with the same phase velocity as the solitary wave. Such a synchronism is possible because of the presence of rotational dispersion. The law of damping is found to be “terminal” in the sense that the solitary wave disappears in a finite time. The radiated wave amplitude and the structure of the radiated “tail” in space–time are also found. Some numerical results, which confirm the approximate theory developed here, are given.