Abstract by Jalen Morgan
J.D. Mireles James
Parameterization method for nonlinear manifolds of PDEs.
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.