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arXiv · 2510.19828

Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves

Michal Shavit·Fabio Pusateri·Zhou Zhang·Yulin Pan·Davide Maestrini·Miguel Onorato·Jalal Shatah
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Abstract

In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements, however, reveal prominent features that go beyond the predictions of time resonance theory. In this work, we develop a theoretical framework to interpret these signatures by identifying and characterizing an alternative mechanism: space resonances. These arise when wave packets share the same group velocity and remain co-located, leading to long-lived interactions. We further show that gauge-breaking terms in the Hamiltonian give rise to space resonances supported on negative frequencies. By combining sea-surface elevation data, numerical simulations, and analytical theory, we derive the leading-order spatio-temporal spectrum for weakly interacting water waves, providing a unified explanation for its observed features.

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Michal Shavit, Fabio Pusateri, Zhou Zhang, Yulin Pan, Davide Maestrini, Miguel Onorato, Jalal Shatah. 2025-10-07. Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves. https://arxiv.org/abs/2510.19828

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