The fourth edition of the prestigious Barcelona Dynamical Systems Prize has been awarded to Massimiliano Berti, Alberto Maspero, and Paolo Ventura of SISSA for their article “Full description of Benjamin-Feir instability of Stokes waves in deep water” published in Inventiones Mathematicae 2022. This international prize, offered by the Catalan Mathematical Society under the patronage of Prof. Carles Simó, has been awarded by an International Jury of five researchers. It recognises significant contributions in the area of Dynamical Systems, published in the years 2019-2023, evaluating new theoretical approaches and methodologies and the relevance of the applications.
The awarded paper addresses a fundamental problem in fluid mechanics: the stability or instability of traveling periodic Stokes waves. In 1967, Benjamin and Feir proposed a famous heuristic mechanism explaining how these waves could become unstable when subjected to long-wave perturbations.
The study by Berti, Maspero, and Ventura provides, for the first time, the complete rigorous demonstration of this instability phenomenon, offering a full description of the splitting of the four eigenvalues near zero in the linearized water wave equations for small-amplitude Stokes solutions. Specifically, the work confirms the conjecture that, as the Floquet exponent varies, a pair of non-purely imaginary eigenvalues traces out a closed figure-eight trajectory.
This highly significant result was achieved by innovatively exploiting the Hamiltonian and reversible nature of the water wave equations, combining advanced techniques from spectral theory and dynamical systems.