Rigorous proof of spectral stability for small non-resonant capillary-gravity waves and Wilton ripples, plus instability index functions near resonances, via periodic Evans function with Weierstrass preparation.
Bridges and Alexander Mielke, A proof of the Benjamin-Feir instability , Arch
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Stable and unstable capillary-gravity waves
Rigorous proof of spectral stability for small non-resonant capillary-gravity waves and Wilton ripples, plus instability index functions near resonances, via periodic Evans function with Weierstrass preparation.