A numerical study of the spectrum of the nonlinear Schrodinger equation

[摘要] The NLS is a universal equation of the class of nonlinear integrable systems. Theaim of this thesis is to study the NLS numerically. More speci cally, an algorithm isdeveloped to calculate its nonlinear spectrum. The nonlinear spectrum is then usedas a diagnostic for numerical studies of the NLS. The spectrum consists of a discretepart, further subdivided into the main part, the auxiliary part, and the continuousspectrum. Two algorithms are developed for calculating the main spectrum. One isbased on Floquet theory,rst implemented by Overman [12]. The other is a directcalculation of the eigenvalues by Herbst and Weideman [16]. These algorithmsare combined through the marching squares algorithm to calculate the continuousspectrum. All ideas are illustrated by numerical examples.

[发布机构] Stellenbosch University