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Modulation equations revisited

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HY2W01 - Modulation theory and dispersive shock waves

Modulation theory as set up by Whitham in the early 1970s has been used for decades to study dispersive wave trains. Yet it remains rooted in algebraic arguments that are valid only for some completely integrable PDEs, and its rigorous justification remains an open problem for most equations. Asymptotic analysis sheds new light on modulation equations in the limiting regimes of harmonic waves, and of solitonic waves. This will be explained in a setting that encompasses an example that is familiar to the audience, namely the nonlinear Schrödinger equation.

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

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