Conference: Symposium about Applied Mathematics


Characterization and Computation of Multiple Unstable (Nontrivial) Solutions to Semilinear Elliptic Systems

{{_Ltalk:R}} Dr. Xianjin Chen
Date: 17.12.09   Time: 09.00 - 10.00   Room: Y27H35/36

Abstract: Exhibiting many novel new phenomena that are not present in the single equation case, systems are much more interesting in many applications. Motivated by the growing experimental observations and studies of various nonlinear vector phenomena (e.g., spatial vector solitons, multi-component Bose-Einstein condensates) arising in diverse physical contexts (e.g., condensed matter physics, nonlinear optics, etc), the speaker will give an overview of some computational theory and methods for finding multiple unstable solutions (e.g., saddle points) to three types of nonlinear variational elliptic systems: cooperative, noncooperative, and Hamiltonian. In particular, two stable methods (called a local min-orthogonal method and a local min-max-orthogonal method) for multiple unstable solutions to variational elliptic systems will be presented. Finally, numerical examples are given to illustrate both methods.