Traveling waves for the nonlinear variational wave equation

Katrin Grunert () and Audun Reigstad ()
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Katrin Grunert: NTNU Norwegian University of Science and Technology
Audun Reigstad: NTNU Norwegian University of Science and Technology

Partial Differential Equations and Applications, 2021, vol. 2, issue 5, 1-21

Abstract: 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.

Keywords: Nonlinear variational wave equation; Traveling waves; Composite waves; Primary 35C07; 35L70; Secondary 35B60 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00116-5

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