BYU

Abstract by Jalen Morgan

Personal Infomation


Presenter's Name

Jalen Morgan

Degree Level

Undergraduate

Co-Authors

Blake Barker
J.D. Mireles James
Christian Reinhardt

Abstract Infomation


Department

Mathematics

Faculty Advisor

Blake Barker

Title

Parameterization method for unstable manifolds of nonlinear waves

Abstract

In previous projects we've worked on, we've identified both stable and unstable wave solutions for various PDEs.  The stable waves are solutions that converge back to a constant shape when perturbed.  The unstable waves, however, lose their shape when even the smallest error is introduced.  In this project we've focused on the unstable waves and how they behave when given a perturbation.  Specifically, we look at the eigenfunction of the waves to evolve them in the direction of greatest instability.  We do this using a parameterization method we designed for the problem.  To confirm the accuracy of our time evolution method, we compare with finite difference approximations.