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Weakly damped KdV soliton dynamics with the random force

Author

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  • Zahibo, N.
  • Pelinovsky, E.
  • Sergeeva, A.

Abstract

The soliton dynamics in the random field is studied in the framework of the Korteweg–de Vries–Burgers equation. Asymptotic solution of this equation with weak dissipation is found and the average wave field is analyzed. All formulas can be given explicitly for the uniform (table-top) distribution function of the random field. Weakly damped KdV soliton on large times transforms to the “thick” soliton or KdV-like soliton depending from the statistical properties of the force. New scenario of KdV soliton transformation into the thick soliton and then again in KdV-like soliton is predicted for certain conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1645-1650
    DOI: 10.1016/j.chaos.2007.06.032
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    References listed on IDEAS

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    1. Liu, Qing, 2007. "Some exact solutions for stochastic mKdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1224-1230.
    2. Chen, Yong & Wang, Qi & Li, Biao, 2005. "The stochastic soliton-like solutions of stochastic KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1465-1473.
    3. Liu, Qing, 2007. "A modified Jacobi elliptic function expansion method and its application to Wick-type stochastic KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1215-1223.
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    Cited by:

    1. Abrashkin, Anatoly, 2019. "Unsteady Gerstner waves," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 152-158.

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