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

Author

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  • Marcelo V. Flamarion

    (Unidade Acadêmica do Cabo de Santo Agostinho, UFRPE/Rural Federal University of Pernambuco, BR 101 Sul, Cabo de Santo Agostinho 54503-900, Brazil
    These authors contributed equally to this work.)

  • Efim Pelinovsky

    (Institute of Applied Physics, 46 Uljanov Str., 603155 Nizhny Novgorod, Russia
    National Research University—Higher School of Economics, 101000 Moscow, Russia
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Marcelo V. Flamarion & Efim Pelinovsky, 2022. "Solitary Wave Interactions with an External Periodic Force: The Extended Korteweg-de Vries Framework," Mathematics, MDPI, vol. 10(23), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4538-:d:989832
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    References listed on IDEAS

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    1. Flamarion, Marcelo V. & Pelinovsky, Efim, 2022. "Soliton interactions with an external forcing: The modified Korteweg–de Vries framework," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
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    Cited by:

    1. Flamarion, Marcelo V. & Pelinovsky, Efim & Didenkulova, Ekaterina, 2023. "Investigating overtaking collisions of solitary waves in the Schamel equation," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Flamarion, Marcelo V. & Pelinovsky, Efim, 2023. "Interactions of solitons with an external force field: Exploring the Schamel equation framework," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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    1. Flamarion, Marcelo V. & Pelinovsky, Efim, 2023. "Interactions of solitons with an external force field: Exploring the Schamel equation framework," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Flamarion, Marcelo V. & Pelinovsky, Efim & Didenkulova, Ekaterina, 2023. "Investigating overtaking collisions of solitary waves in the Schamel equation," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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