Benjamin–Feir instability of Stokes waves

  • Massimiliano Berti

    SISSA, Trieste, Italy
  • Alberto Maspero

    SISSA, Trieste, Italy
  • Paolo Ventura

    SISSA, Trieste, Italy
Benjamin–Feir instability of Stokes waves cover
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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.

Cite this article

Massimiliano Berti, Alberto Maspero, Paolo Ventura, Benjamin–Feir instability of Stokes waves. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 2, pp. 399–412

DOI 10.4171/RLM/975