BYU

Abstract by Jalen Morgan

Personal Infomation


Presenter's Name

Jalen Morgan

Degree Level

Undergraduate

Co-Authors

Blake Barker
J.D. Mireles James

Abstract Infomation


Department

Mathematics

Faculty Advisor

Blake Barker

Title

Parameterization method for nonlinear manifolds of PDEs.

Abstract

We develop a method for parameterizing nonlinear manifolds of PDEs near stationary solutions. We apply this method to the Nagumo equation, Gray-Scott's equations, and Schrodinger's equation. Specifically, we solve for the nonlinear manifold that converges to an unstable traveling wave solution in backward time in the direction of the eigenfunction. We discuss the problem of correctly implementing boundary conditions with the oscillatory eigenfunction that comes from Schrodinger's equation.