On Existence and Uniqueness Results for some Nonlinear Schrödinger equations

The (nonlinear) behaviour of laser beams can be described with Nonlinear Schrödinger equations (NLS). The purpose of this thesis is to shed light on two mathematical papers that give existence and uniqueness results for an NLS equation called the soliton equation. The contribution is to expand the level of detail with which the analysis and some...

Identification of Spines in Nonlinear Fourier Spectra for the Periodic Nonlinear Schrödinger Equation: Internship WI5118 - Report

The nonlinear Fourier transform for the focusing periodic nonlinear Schrodinger equation is investigated. This paper is focused on the approximation of the spines in the nonlinear spectrum using results from Floquet theory. Algorithms for the numerical computation of the spines based on the Fourier collocation method are...

A Stochastic Parametrically-Forced NLS Equation

In this thesis, a variation on the nonlinear Schrödinger (NLS) equation with multiplicative noise is studied. In particular, we consider a stochastic version of the parametrically-forced nonlinear Schrödinger equation (PFNLS), which models the effect of linear loss and the compensation thereof by phase-sensitive amplification in pulse...

Computing the Spectrum of the Confined Hydrogen Atom

This thesis is about the numerical approximation of the spectrum of the confined hydrogen atom. The energy levels and wave functions of the hydrogen atom are modelled by the corresponding eigenvalues and eigenvectors of the Schrödinger equation with Coulomb potential. At first different discretisation techniques for the hydrogenic Schrödinger...

A nonlinear Schrödinger equation in L² with multiplicative white noise

In this thesis existence and uniqueness of the solution of a nonlinear Schrödinger equation in L² with multiplicative white noise is proven under some assumptions. Furthermore, pathwise L²-norm conservation of the solution is studied.