A numerical study of the spectrum of the nonlinear Schrodinger equation

dc.contributor.advisorHerbst, B. M.
dc.contributor.advisorBarashenkov, I. V.
dc.contributor.authorOlivier, Carel Petrus
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics.
dc.descriptionThesis (MSc (Mathematical Sciences. Applied Mathematics))--Stellenbosch University, 2008.
dc.description.abstractThe NLS is a universal equation of the class of nonlinear integrable systems. The aim of this thesis is to study the NLS numerically. More speci cally, an algorithm is developed to calculate its nonlinear spectrum. The nonlinear spectrum is then used as a diagnostic for numerical studies of the NLS. The spectrum consists of a discrete part, further subdivided into the main part, the auxiliary part, and the continuous spectrum. Two algorithms are developed for calculating the main spectrum. One is based on Floquet theory, rst implemented by Overman [12]. The other is a direct calculation of the eigenvalues by Herbst and Weideman [16]. These algorithms are combined through the marching squares algorithm to calculate the continuous spectrum. All ideas are illustrated by numerical examples.en
dc.publisherStellenbosch : Stellenbosch University
dc.subjectNonlinear Schrodinger equationen
dc.subjectNonlinear spectrumen
dc.subjectDissertations -- Applied mathematicsen
dc.subjectTheses -- Applied mathematicsen
dc.subjectGross-Pitaevskii equationsen
dc.titleA numerical study of the spectrum of the nonlinear Schrodinger equationen
dc.rights.holderStellenbosch University

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