We overview the recent result [3, Theorem 1.1] about the high-frequency instability of pure gravity Stokes waves subject to longitudinal perturbations. The spectral bands of unstable eigenvalues away from the origin form a sequence of isolas parameterized by an integer p≥2 for any value of the depth h>0 such that an explicit coefficient β1(p)(h) is not zero. In [3] it is proved that the map h↦β1(p)(h) is analytic and it is not identically zero for any p≥2, by showing that limh→0+β1(p)(h)=-∞. In this manuscript we compute the asymptotic expansion of β1(p)(h)in the deep-water limit h→+∞ –it vanishes exponentially fast to zero– for p=2, 3, 4.
Berti, M., Corsi, L., Maspero, A., Ventura, P. (2026). On higher order isolas of unstable stokes waves. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 19(2), 493-512 [10.1007/s40574-025-00500-8].
On higher order isolas of unstable stokes waves
Corsi, Livia;
2026-01-01
Abstract
We overview the recent result [3, Theorem 1.1] about the high-frequency instability of pure gravity Stokes waves subject to longitudinal perturbations. The spectral bands of unstable eigenvalues away from the origin form a sequence of isolas parameterized by an integer p≥2 for any value of the depth h>0 such that an explicit coefficient β1(p)(h) is not zero. In [3] it is proved that the map h↦β1(p)(h) is analytic and it is not identically zero for any p≥2, by showing that limh→0+β1(p)(h)=-∞. In this manuscript we compute the asymptotic expansion of β1(p)(h)in the deep-water limit h→+∞ –it vanishes exponentially fast to zero– for p=2, 3, 4.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
