Traveling Water Waves - The Ebb and Flow of Two Centuries

Susanna V. Haziot, Vera Mikyoung Hur, Walter A. Strauss, J. F. Toland, Erik WahlEn, Samuel Walsh, Miles H. Wheeler

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)317-401
JournalQuarterly of Applied Mathematics
Issue number2
Publication statusPublished - 2022

Subject classification (UKÄ)

  • Physical Sciences


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