Quasi-periodic water waves

Date: 
Friday, March 26, 2021 - 3:00pm
Location: 
Zoom
Speaker: 
Jon Wilkening

Abstract: We present a framework to compute and study two-dimensional water waves that are quasi-periodic in space and/or time. This means they can be represented as periodic functions on a higher-dimensional torus by evaluating along irrational directions. In the spatially quasi-periodic case, the nonlocal Dirichlet-Neumann operator is computed using conformal mapping methods and a quasi-periodic variant of the Hilbert transform. In the temporally quasi-periodic case, we devise a shooting method to compute standing waves with 3 quasi-periods as well as hybrid traveling-standing waves that return to a spatial translation of their initial condition at a later time. Many examples will be given to illustrate the types of behavior that can occur.

Please access the talk through the Research Seminars page ( https://researchseminars.org/seminar/MO_Analysis ); you will need to register for a free account. If you have any difficulty, please contact Samuel Walsh (walshsa@missouri.edu).