Communication Dans Un Congrès Année : 2022

Kirk Lecture: Periodic waves, stability and modulations

Résumé

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, the various notions of stability attached to them, and 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.

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hal-04798172 , version 1 (22-11-2024)

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  • HAL Id : hal-04798172 , version 1

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Sylvie Benzoni-Gavage. Kirk Lecture: Periodic waves, stability and modulations. Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves, Gennady El, University Mark Hoefer, Antonio Moro, Barbara Prinari, Michael Shearer, Jul 2022, Cambridge (Isaac Newton Institute for Mathematical Sciences), France. ⟨hal-04798172⟩
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