Document Type
Article
Publication Date
4-20-2026
Abstract
We study the spectral stability of small-amplitude Stokes waves in a family of weakly nonlinear, unidirectional models of the form ut + Lu + (u2)x = 0. We introduce a perturbation method to expand the spectral data in wave amplitude near flat-state eigenvalue collisions, with the ratio of the colliding modes as a free parameter. This yields sheets of spectral data whose slices at fixed amplitude give isolas of instability. The same perturbation framework treats both high-frequency and Benjamin--Feir instabilities, extends to discontinuous dispersion relations (including the Akers--Milewski equation), and, for the first time, provides an analytic approximation of the Benjamin--Feir spectrum for this model and a direct comparison of high-frequency and Benjamin--Feir growth rates across the full family of models. Asymptotic predictions are validated against numerical spectra computed by Floquet--Fourier--Hill and quasi-Newton methods.
Source Publication
Water Waves (ISSN 2523-367X | eISSN 2523-3688)
Recommended Citation
Akers, B., Creedon, R. Sheets of Spectral Data of Stokes Waves in Weakly Nonlinear Models. Water Waves 8, 47–70 (2026). https://doi.org/10.1007/s42286-026-00132-1
Comments
© 2026 The Authors.
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