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Solitary Wave Interactions with an External Periodic Force: The Extended Korteweg-de Vries Framework

Mathematics. 2022. Vol. 10. No. 23. Article 4538.
Flamarion M. V., Pelinovsky E.

In this work we asymptotically and numerically studied the interaction of large amplitude
solitary waves with an external periodic force using the forced extended Korteweg-de Vries equation
(feKdV). Regarding these interactions, we found three types of regimes depending on the amplitude
of the solitary wave and how its speed and the speed of the external force are related. A solitary wave
can remain steady when its crest and the crest of the external force are in phase, it can bounce back
and forth remaining close to its initial position when its speed and the external force speed are near
resonant, or it can move away from its initial position without reversing its direction. Additionally,
we verified that the numerical results agreed qualitatively well within the asymptotic approximation
theory for external broad forces.

Research target: Mathematics
Language: English
Full text
DOI
Text on another site
Keywords: солитонsolitonуравнение Кортевега-де ВризаKorteweg-de Vries equation
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