Mathematical Sciences: Dynamics of Pulses in Nonlinear Optical Waveguides

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In the work supported by this award the principal investigator will extend some of his work on the infinite-line Kaup-Newell perturbation theory for a single soliton solution of a nonlinear Schroedinger system to the multiple soliton case. This work has applications to the transmission of data in the form of wave packets through nonlinear optical fibers, and so such it is highly relevant to the design of modern communications' systems that utilize optical fiber technology. The principal investigator will employ methods based upon asymptotics in order to study the behavior of solutions of nonlinear systems of partial differential equations. Every day, it seems, there are articles in the newspapers about the use of fiber optics technologies in the design of modern communications systems. Indeed, telephone companies and computer companies are very much interested in designing "lossless" ways of transmitting data. One possible solution is the emerging technologies based upon fiber optics, since fiber optics affords the potential of transmitting data without significant dispersion or distortion. With this award the principal investigator will study solutions of the nonlinear system of equations that describes the propagation of waves through optical fibers.