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Boaz Ilan, Department of Applied Mathematics, University of California Merced

Generalized Whitham modulation theory

The Korteweg-De Vries (KdV) equation is a universal model for nonlinear dispersive waves. It describes approximately the dynamics of shallow water waves and other systems. G.B. Whitham developed an asymptotic theory to describe slowly-varying periodic solutions of the KdV equation. However, real waves are often subject to peaking and other phenomena that are not described by this model. I will discuss a generalization of Whitham’s theory and its application to models with higher-order dispersion and nonlinearity.
These are joint works with Adam Binswanger, Mark Hoefer, and Patrick Sprenger.

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