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02/19/02 Colloquium
DR. CONSTANCE SCHOBER
DEPARTMENT OF MATHEMATICS
OLD DOMINION UNIVERSITY
DEPARTMENT OF MATHEMATICS
OLD DOMINION UNIVERSITY
CHAOTIC DYNAMICS IN NONLINEAR WAVES: COMPUTATIONAL AND PHYSICAL
Abstract: In this talk I will discuss the chaotic wave dynamics associated with perturbed, dispersive, nonlinear Schrodinger (NLS) equations with periodic boundary conditions. The chaotic evolution resulting from discretization, i.e. computational chaos, is described in detail. Laboratory and numerical experiments will then be presented which demonstrate that irregular wave dynamics is also associated with the well known physical problems of water waves and nonlinear optics and that it has a universal characterization. A Floquet spectral analysis of both the perturbed NLS numerical data and of the laboratory data establishes that left-right homoclinic excitations occur, i.e., the waveform exhibits random bifurcations across standing wave states to left and right going modulated traveling waves. This study provides the first physical realization of the chaotic behavior predicted by our analytical work on perturbed NLS equations.