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Numerical study of traveling-wave solutions for the Camassa–Holm equation

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  • Kalisch, Henrik
  • Lenells, Jonatan

Abstract

We explore numerically different aspects of periodic traveling-wave solutions of the Camassa–Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied.

Suggested Citation

  • Kalisch, Henrik & Lenells, Jonatan, 2005. "Numerical study of traveling-wave solutions for the Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 287-298.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:2:p:287-298
    DOI: 10.1016/j.chaos.2004.11.024
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    Cited by:

    1. Shijie Zeng & Yaqing Liu, 2023. "The Whitham Modulation Solution of the Complex Modified KdV Equation," Mathematics, MDPI, vol. 11(13), pages 1-18, June.
    2. Abbasbandy, S. & Parkes, E.J., 2008. "Solitary smooth hump solutions of the Camassa–Holm equation by means of the homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 581-591.
    3. Yin, Jiuli & Tian, Lixin, 2009. "Stumpons and fractal-like wave solutions to the Dullin–Gottwald–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 643-648.
    4. A. A. Alderremy & Hassan Khan & Rasool Shah & Shaban Aly & Dumitru Baleanu, 2020. "The Analytical Analysis of Time-Fractional Fornberg–Whitham Equations," Mathematics, MDPI, vol. 8(6), pages 1-14, June.
    5. Yuheng Jiang & Yu Tian & Yao Qi, 2024. "Solitary Wave Solutions of a Hyperelastic Dispersive Equation," Mathematics, MDPI, vol. 12(4), pages 1-10, February.
    6. Parkes, E.J., 2008. "Some periodic and solitary travelling-wave solutions of the short-pulse equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 154-159.
    7. Xianguo Geng & Ruomeng Li, 2019. "On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation," Mathematics, MDPI, vol. 7(10), pages 1-23, October.
    8. Katrin Grunert & Audun Reigstad, 2021. "Traveling waves for the nonlinear variational wave equation," Partial Differential Equations and Applications, Springer, vol. 2(5), pages 1-21, October.
    9. Hendrik Ranocha & Manuel Quezada Luna & David I. Ketcheson, 2021. "On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations," Partial Differential Equations and Applications, Springer, vol. 2(6), pages 1-26, December.
    10. Parkes, E.J. & Vakhnenko, V.O., 2005. "Explicit solutions of the Camassa–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1309-1316.

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