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Traveling waves for the nonlinear variational wave equation

Author

Listed:
  • Katrin Grunert

    (NTNU Norwegian University of Science and Technology)

  • Audun Reigstad

    (NTNU Norwegian University of Science and Technology)

Abstract

We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and constant segments, glued together at points where at least one one-sided derivative is unbounded. Applying the method of proof to the Camassa–Holm equation, we recover some well-known results on its traveling wave solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:pardea:v:2:y:2021:i:5:d:10.1007_s42985-021-00116-5
    DOI: 10.1007/s42985-021-00116-5
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    References listed on IDEAS

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    1. 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.
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