Traveling water waves — the ebb and flow of two centuries

Haziot, Susanna; Hur, Vera; Strauss, Walter; Toland, J.; Wahlén, Erik; Walsh, Samuel; Wheeler, Miles

doi:10.1090/qam/1614

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Traveling water waves — the ebb and flow of two centuries

Authors: Susanna V. Haziot, Vera Mikyoung Hur, Walter A. Strauss, J. F. Toland, Erik Wahlén, Samuel Walsh and Miles H. Wheeler
Journal: Quart. Appl. Math. 80 (2022), 317-401
MSC (2020): Primary 35Q35, 35Q31, 76B15, 76B25, 76B47
DOI: https://doi.org/10.1090/qam/1614
Published electronically: March 14, 2022
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Abstract: This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical studies of periodic waves with critical layers that may overhang; existence, nonexistence, and qualitative theory of solitary waves and fronts; traveling waves with localized vorticity or density stratification; and waves in three dimensions.

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