Abstract
The problem of modelling nonlinear wave phenomena, despite 150 years of progress, is still far from resolved. For the Korteweg-de Vries equation, though nonlinear, has regular solutions for all time, given regular initial data. That is, singularities do not form under the evolution governed by the KdV equation. This fact must be reconciled with G. Stokes’ remarkable prediction of the wave of greatest height. Stokes’ conjecture has been only recently been proved rigorously for the exact equations by Toland, [73], and Amick, Fraenkel, and Toland [4].
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© 1998 Springer Basel AG
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Cercignani, C., Sattinger, D.H. (1998). Weak and Strong Nonlinearities. In: Scaling Limits and Models in Physical Processes. DMV Seminar, vol 28. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8810-3_9
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DOI: https://doi.org/10.1007/978-3-0348-8810-3_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-5985-0
Online ISBN: 978-3-0348-8810-3
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