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Numerical Solution of Riemann Hilbert Problems Applied to High Speed Communication

Modeling, Computation, Nonlinearity, Randomness and Waves Seminar

Numerical Solution of Riemann Hilbert Problems Applied to High Speed Communication
Series: Modeling, Computation, Nonlinearity, Randomness and Waves Seminar
Location: MATH 402
Presenter: Joe Gibney, Program in Applied Mathematics, University of Arizona

The main achievement of the last decade in the field of high-speed information transmission is the technology of optical coherent communication. This technology is based on the linear regime of pulse dynamics in optical fibers. With increasing transmission speed and distance (long-haul communications) coherent systems are experiencing the negative effects of fiber nonlinearity. For currently existing optical fibers and optical pulse parameters, the pulse dynamics are well described by the nonlinear Schrodinger equation (NLS). Recently it has been proposed to utilize the linear transmission of the scattering data for the Lax operator associated with the NLS to overcome limitations caused by nonlinearity in coherent systems. In this talk, we develop a method for computing scattering data and recovering the data signal from back-processed scattering data using the solution of the associated Riemann-Hilbert problem, which is solved with a fast and accurate numerical method.