INVERSE SCATTERING TRANSFORM AND SOLITONS FOR MATRIX NONLINEAR SCHRODINGER SYSTEMS AND FOR THE DEFOCUSING ABLOWITZ-LADIK EQUATION WITH NONZERO BOUNDARY CONDITIONS
The scalar nonlinear Schrodinger (NLS) equation is a nonlinear partial differential equation that models many of the world’s weakly nonlinear dispersive wave phenomena. This dissertation discusses two important variants of NLS: (i) the matrix NLS (MNLS), applicable in low-temperature physics and nonlinear optics, and (ii) the defocusing Ablowitz-Ladik equation, a variant of scalar NLS, continuous in time but discrete in space. In Chapter 2, the Inverse Scattering Transform (IST) is used to investigate four distinct MNLS systems, proposed by Tsuchida, shown to be integrable and to have solitary ...
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