We are pleased to announce that the article “Full description of Benjamin-Feir instability of Stokes waves in deep water” by Massimiliano Berti and Alberto Maspero, Full Professors of Mathematical Analysis at SISSA, coauthored with SISSA alumnus Paolo Ventura and published in Inventiones Mathematicae in 2022, has received the prestigious 2025 Frontiers of Science Award in Mathematics.
Inaugurated in 2023 by the International Congress of Basic Sciences (ICBS), this prestigious annual award recognises groundbreaking research papers in the basic sciences. The paper by Berti, Maspero and Ventura has been awarded for its notable contributions in the field of Partial Differential Equations.
This work addresses a central and long-standing question in fluid mechanics: the stability or instability of travelling 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 article provides the first complete and rigorous proof of this instability mechanism. Through a sophisticated combination of spectral theory and dynamical systems techniques, the authors fully describe the Floquet spectral bands near zero of the linearised water wave operator at small-amplitude Stokes waves. In particular, their 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 landmark result was achieved by exploiting the Hamiltonian and reversible structure of the water wave equations, combined with advanced tools from spectral theory and dynamical systems.
The official award ceremony will take place during the International Congress of Basic Sciences in Beijing, in July 2025, a major global gathering of leading figures across the mathematical and physical sciences.