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Auto-resonance process under the interaction of solitons with external force and dissipation

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  • Flamarion, Marcelo V.
  • Pelinovsky, Efim

Abstract

Algebraic soliton interactions with an external force in the presence of Reynolds viscosity is investigated. In the absence of an external force, the soliton amplitude decays over time. However, when an external force is introduced, it acts as a restoring force, and in some cases, the soliton’s amplitude is preserved. A dynamical system that governs the soliton amplitude and its crest position is obtained assuming a weak force and weak viscosity. For an external force with a Gaussian shape, the dynamical system has two equilibrium points, namely, a saddle and a stable spiral. Asymptotic results are compared with direct numerical simulations, and a strong qualitative agreement is observed. The stable spiral predicted by the asymptotic theory is stable in the sense that soliton solutions with a chosen amplitude and crest position near the spiral point are attracted to it, preserving their amplitude and location.

Suggested Citation

  • Flamarion, Marcelo V. & Pelinovsky, Efim, 2024. "Auto-resonance process under the interaction of solitons with external force and dissipation," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p2:s0960077924012645
    DOI: 10.1016/j.chaos.2024.115712
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    References listed on IDEAS

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    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. Pawan Negi & Trilochan Sahoo & Niharika Singh & Yury Stepanyants, 2023. "Dynamics of Benjamin–Ono Solitons in a Two-Layer Ocean with a Shear Flow," Mathematics, MDPI, vol. 11(15), pages 1-15, August.
    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).
    4. Zahibo, N. & Pelinovsky, E. & Sergeeva, A., 2009. "Weakly damped KdV soliton dynamics with the random force," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1645-1650.
    5. 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. Kochurin, E.A., 2025. "Anisotropy of free-surface wave turbulence induced by a horizontal magnetic (electric) field," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    2. Flamarion, Marcelo V. & Pelinovsky, Efim & Melnikov, Ioann, 2025. "Spring–mass behavior of solitons under the influence of an external force field within the modified Korteweg–de Vries equation," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).

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