Nonlinear Wave Propagation
Final rept. 1 Dec 1999-30 Nov 2002
COLORADO UNIV AT BOULDER DEPT OF APPLIED MATHEMATICS
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Research investigations involving the nonlinear wave propagation that arise in physically significant systems have been carried out Applications include modeling and computational studies of wave phenomena in nonlinear optics, solutions of physically significant nonlinear equations, chaotic wave dynamics in physical systems and inverse scattering. There have been a number of important research contributions. During the past three years 19 papers were published or accepted for publication in refereed journals, 4 book chapters were published or accepted, and 14 invited lectures were given. New methods to find solutions to discrete equations in a nonlinear optical fiber array were discovered. Discrete diffraction managed systems and associated solitons were proposed. This work is relevant to recent experiments involving discrete optical waveguides. Experimental arrays occupy 5 microns in width and a total length of 2-5 millimeters. From first principles, the equations governing discrete systems in nonlinear optical arrays as well as discrete diffraction managed systems have been derived. The concept of dispersion management is being applied to the study of ultra-short laser pulse dynamics in Tisapphire lasers In quadratic nonlinear optical media, a vector system of nonlinear Schrodinger NLS type with coupling to a mean field has been derived. It has been established that a universal type of chaotic wave dynamics can develop in physical sand computational systems. Parameter regimes have been delineated where chaotic dynamics are predicted and observed. Such chaotic dynamics has been shown to arise in computational chaos, water waves and short pulses in nonlinear optical fibers. A class of free boundary problems has been investigated. New classes of localized solutions to multidimensional nonlinear wave problems have been obtained and analyzed.
- Numerical Mathematics
- Fluid Mechanics