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Interaction of a Solitary Wave with an External Force Moving with Variable Speed
Author(s) -
Grimshaw Roger,
Pelinovsky Efim,
Sakov Pavel
Publication year - 1996
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 - 10.1002/sapm1996973235
Subject(s) - acceleration , amplitude , phase portrait , physics , sign (mathematics) , forcing (mathematics) , constant (computer programming) , classical mechanics , damped wave , korteweg–de vries equation , position (finance) , mathematical analysis , wave equation , mechanics , mathematics , bifurcation , nonlinear system , quantum mechanics , finance , computer science , economics , programming language
The interaction of a solitary wave with an external force moving with constant acceleration is studied within the forced Korteweg‐de Vries equation. For the case of a weak isolated force an asymptotic model based on equations for the amplitude and position of the solitary wave is developed. Phase portraits for this asymptotic system are obtained analytically and numerically. Analysis has shown that an accelerated force of either sign can capture a solitary wave if the acceleration is less than a certain critical value, depending on the forcing amplitude (for the case of a constant force speed only a positive force can capture a solitary wave). Direct numerical simulation of the forced Korteweg‐de Vries equation has confirmed the predictions of the asymptotic model. Also, it is shown numerically that the accelerated force can capture more than one solitary wave.