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Higher-Order Isolas in the Spectral Instability of Stokes Water Waves

How the linearized spectrum of a Stokes wave, beyond the low-frequency Benjamin-Feir instability, contains higher bands of unstable eigenvalues called isolas, indexed by an integer p >= 2 and controlled by an analytic coefficient that depends on water depth. How that coefficient behaves in the deep-water limit for p = 2, 3, 4, where it decays exponentially, complementing its shallow-water blow-up.

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On higher order isolas of unstable Stokes waves Massimiliano Berti, Livia Corsi, Alberto Maspero

Stokes waves are the classical periodic traveling-wave solutions of the two-dimensional gravity water-wave equations. Small-amplitude Stokes waves in sufficiently deep water are unstable under long-w…