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Kirk Lecture: Periodic waves, stability and modulations

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HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

Rooted in Poincaré’s work regarding the stability of the Solar System, the qualitative analysis of periodic solutions to Hamiltonian dynamical systems is still an active field of research, especially in infinite dimensions, either for lattice dynamical systems or partial differential equations. The talk will concentrate on periodic waves, which are periodic in both space and time, on the various notions of stability attached to them, and on their modulations. Widely used in electronics and telecommunications, modulations yield many open questions in maths. I will show indeed that the modulation theory coined by Whitham more than fifty years ago still awaits rigorous results as soon as we depart from an integrable context.

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

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