Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909947101446144 |
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| author | Shavit, Michal Pusateri, Fabio Zhang, Zhou Pan, Yulin Maestrini, Davide Onorato, Miguel Shatah, Jalal |
| author_facet | Shavit, Michal Pusateri, Fabio Zhang, Zhou Pan, Yulin Maestrini, Davide Onorato, Miguel Shatah, Jalal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves Shavit, Michal Pusateri, Fabio Zhang, Zhou Pan, Yulin Maestrini, Davide Onorato, Miguel Shatah, Jalal Pattern Formation and Solitons Mathematical Physics Chaotic Dynamics Fluid Dynamics 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. |
| title | Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves |
| topic | Pattern Formation and Solitons Mathematical Physics Chaotic Dynamics Fluid Dynamics |
| url | https://arxiv.org/abs/2510.19828 |