Signal processing and communication with solitons

Traditional signal processing algorithms rely heavily on models that are inherently linear. Such models are attractive both for their mathematical tractability and their applicability to the rich class of signals that can be represented with Fourier methods. Nonlinear systems that support soliton solutions share many of the properties that make linear systems attractive from an engineering standpoint. Although nonlinear, these systems are solvable through inverse scattering, a technique analogous to the Fourier transform for linear systems. Solitons are eigenfunctions of these systems which satisfy a nonlinear form of superposition and display rich signal dynamics as they interact. By using solitons for signal synthesis, the corresponding nonlinear systems become specialized signal processors which are naturally suited to a number of complex signal processing tasks. Specific analog circuits can generate soliton signals and can be used as natural multiplexers and demultiplexers in a number of potential soliton-based wireless communication applications. These circuits play an important role in investigating the effects of noise on soliton behavior. Finally, the soliton signal dynamics also provide a mechanism for decreasing transmitted signal energy while enhancing signal detection and parameter estimation performance. Thesis Supervisor: Alan V. Oppenheim Title: Distinguished Professor of Electrical Engineering and Computer Science