Speaker: YongJun Yuan
Beijing Computational Science Research Center

Abstract:  Multiple unstable solutions, lowly or highly, singly or multiply excited, to many nonlinear systems have been observed and mathematically proved to exist and have a variety of configurations, instabilities/maneuverabilities. They used to be considered too hard/elusive to catch and therefore to apply. Now scientists are able to induce, reach or control them with new advanced (synchrotronic, laser) technologies and search for NEW applications. To numerically solve these unstable solutions with a stable method, a modified local minimax method (MLMM) is proposed in the report. The convergence results for the algorithm as well as the exact value of a critical perturbation value for a singurly perturbed Neumann problem are also disscussed. Many interesting numerical solutions are computed and displayed with their contours and mesh profiles to illustrate the theory and method.