We present the recent results in Berti et al. [Invent. Math. (2022), to appear] regarding the Benjamin-Feir instability of small amplitude Stokes waves in deep water. We completely describe the behavior of the four eigenvalues close to zero of the linearized water waves equations at the Stokes solution, as the Floquet exponent is turned on, proving the conjecture that a pair of non-purely imaginary eigenvalues depicts a closed figure "8", in full agreement with numerical simulations.
Benjamin-Feir instability of Stokes waves / Berti, M; Maspero, A; Ventura, P. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 33:2(2022), pp. 399-412. [10.4171/RLM/975]
Benjamin-Feir instability of Stokes waves
Berti, M
Membro del Collaboration group
;Maspero, A;Ventura, PMembro del Collaboration group
2022-01-01
Abstract
We present the recent results in Berti et al. [Invent. Math. (2022), to appear] regarding the Benjamin-Feir instability of small amplitude Stokes waves in deep water. We completely describe the behavior of the four eigenvalues close to zero of the linearized water waves equations at the Stokes solution, as the Floquet exponent is turned on, proving the conjecture that a pair of non-purely imaginary eigenvalues depicts a closed figure "8", in full agreement with numerical simulations.| File | Dimensione | Formato | |
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