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Features of the interaction of paired solitary waves with the Cubic Vortical Whitham equation

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  • Flamarion, Marcelo V.
  • Pelinovsky, Efim

Abstract

In this article, we consider the cubic vortical Whitham equation with both positive and negative nonlinearity to investigate overtaking solitary wave collisions. We compute solitary waves numerically, including “thick” solitary waves. Our results show that in both cases, the geometric Lax categorization holds, however, it is independent of the magnitude of the amplitude of the solitary waves. Besides, for negative cubic nonlinearity, we compute thick solitary waves and investigate their paired interactions. Moreover, we show that Gardner solitons and CV-Whitham solitary waves have nearly the same shape and speed when the sign of cubic nonlinearity term is negative.

Suggested Citation

  • Flamarion, Marcelo V. & Pelinovsky, Efim, 2025. "Features of the interaction of paired solitary waves with the Cubic Vortical Whitham equation," Applied Mathematics and Computation, Elsevier, vol. 493(C).
    • Handle: RePEc:eee:apmaco:v:493:y:2025:i:c:s0096300324007264
    DOI: 10.1016/j.amc.2024.129265
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    References listed on IDEAS

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    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. Garayshin, V.V. & Harris, M.W. & Nicolsky, D.J. & Pelinovsky, E.N. & Rybkin, A.V., 2016. "An analytical and numerical study of long wave run-up in U-shaped and V-shaped bays," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 187-197.
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