Terminal Damping of a Solitary Wave Due to Radiation in Rotational Systems |
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Authors: | R H J Grimshaw J-M He & L A Ostrovsky |
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Institution: | Monash University,;University of Colorado |
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Abstract: | 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. |
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