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Nearly time-periodic water waves

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Theory of Water Waves

We compute new families of time-periodic and quasi-periodic solutions of the free-surface Euler equations involving standing waves, standing-traveling waves and collisions of solitary waves of various types. In the collision case, similarities notwithstanding, the new solutions are found to be well outside of the KdV and NLS regimes. A Floquet analysis shows that many of the new solutions are linearly stable to harmonic perturbations. Evolving such perturbations (nonlinearly) over tens of thousands of cycles suggests that the solutions remain nearly time-periodic forever. Parts of the talk will serve as an introduction to later talks in the session.

This talk is part of the Isaac Newton Institute Seminar Series series.

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