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On the long-time behaviour of soliton ensembles

Author

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  • Salupere, A.
  • Engelbrecht, J.
  • Peterson, P.

Abstract

The paper is focused on the details of the emergence of Korteweg–de Vries (KdV) solitons from an initial harmonic excitation. Although the problem is a classical one, numerical simulations over a large range of dispersion parameters in the long run have demonstrated new features: the existence of soliton ensembles including also virtual (hidden) solitons and the periodic patterns of the wave-profile maxima.

Suggested Citation

  • Salupere, A. & Engelbrecht, J. & Peterson, P., 2003. "On the long-time behaviour of soliton ensembles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 137-147.
    • Handle: RePEc:eee:matcom:v:62:y:2003:i:1:p:137-147
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    Citations

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    Cited by:

    1. Christov, Ivan C., 2012. "Hidden solitons in the Zabusky–Kruskal experiment: Analysis using the periodic, inverse scattering transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(6), pages 1069-1078.
    2. Christov, Ivan, 2009. "Internal solitary waves in the ocean: Analysis using the periodic, inverse scattering transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 192-201.
    3. Tamm, Kert & Salupere, Andrus, 2012. "On the propagation of 1D solitary waves in Mindlin-type microstructured solids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(7), pages 1308-1320.
    4. Ilison, Lauri & Salupere, Andrus, 2009. "Propagation of sech2-type solitary waves in hierarchical KdV-type systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3314-3327.
    5. You, Xiangcheng & Xu, Hang & Sun, Qiang, 2022. "Analysis of BBM solitary wave interactions using the conserved quantities," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    6. Yan, Guangwu & Zhang, Jianying, 2009. "A higher-order moment method of the lattice Boltzmann model for the Korteweg–de Vries equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1554-1565.

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