Benjamin Akers: Dimension breaking and numerical continuation

Submitted by Jorge Cisneros on

Speaker: Benjamin Akers, Air Force Institute of Technology

Date: February 13, 2020

Title: Dimension breaking and numerical continuation

Abstract: In this talk, a method for computing large amplitude overturned three dimensional traveling waves will be discussed. The method is based on a dimension-breaking numerical continuation procedure. Both standard continuation methods for computing traveling waves and the dimension-breaking approach will be presented. The primary difficulty in dimension breaking is in constructing an asymptotic solution for weakly three-dimensional solutions. The structure of the governing equations for this asymptotic solution will be discussed, as well as a solution procedure for systems like the water wave problem.