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Soliton interactions with an external forcing: The modified Korteweg–de Vries framework

Author

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  • Flamarion, Marcelo V.
  • Pelinovsky, Efim

Abstract

The aim of this work is to study asymptotically and numerically the interaction of solitons with an external forcing with a variable speed using the forced modified Korteweg–de Vries equation (mKdV). We show that the asymptotic predictions agree well with numerical solutions for forcings with constant speed and linear variable speed. Regarding forcing with linear variable speed, we find regimes in which the solitons are trapped at the external forcing and its amplitude increases or decreases in time depending on whether the forcing accelerates or decelerates.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922010682
    DOI: 10.1016/j.chaos.2022.112889
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    Cited by:

    1. 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.
    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).
    3. 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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