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.

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.