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Applied Mathematics Colloquium

Friday, November 16, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Coherent Structures and Energy Transfer in Conservative Nonlinear Systems

Michael Weinstein

Department of Applied Physics and Applied Mathematics

Columbia University

New York, NY

Abstract

Many nonlinear dispersive conservative systems support coherent structures, e.g. solitary waves, vortices, kinks, which are dominant carriers of energy. Typical initial data resolve, as time advances, into coherent structures plus a decay remainder. A detailed study of this asymptotic resolution reveals that the intermediate time and infinite time dynamics are dominated by interaction and energy transfer among: (i) evolving coherent structures, (ii) dispersive waves and (iii) resonance-induced meta-stable (long lived but time-decaying) states. We shall explain the mathematical tools required to study such interactions and energy transfer. Finally, we present a prediction and experimental confirmation in nonlinear optics.