published_or_final_version / abstract / toc / Physics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 102-120).

We are concerned with the quantum inverse scattering problem. The corresponding Marchenko integral equation is solved by using the collocation method together with piece-wise polynomials, namely, Hermite splines. The scarcity of experimental data and the lack of phase information necessitate the generation of the input reflection coefficient by choosing a specific profile and then applying our method to reconstruct it. Various aspects of the single and coupled channels inverse problem and details about the numerical techniques employed are discussed. We proceed to apply our approach to synthetic seismic reflection data. The transformation of the classical one-dimensional wave equation for elastic displacement into a Schr¨odinger-like equation is presented. As an application of our method, we consider the synthetic reflection travel-time data for a layered substrate from which we recover the seismic impedance of the medium. We also apply our approach to experimental seismic reflection data collected from a deep water location in the North sea. The reflectivity sequence and the relevant seismic wavelet are extracted from the seismic reflection data by applying the statistical estimation procedure known as Markov Chain Monte Carlo method to the problem of blind deconvolution. In order to implement the Marchenko inversion method, the pure spike trains have been replaced by amplitudes having a narrow bell-shaped form to facilitate the numerical solution of the Marchenko integral equation from which the underlying seismic impedance profile of the medium is obtained. / Physics / D.Phil.(Physics)

We clear up two issues regarding the eigenvalue problem for the Manakov system; these problems relate directly to the existence of the soliton [sic] effect in fiber optic cables. The first issue is a bound on the eigenvalues of the Manakov system: if the parameter ξ is an eigenvalue, then it must lie in a certain region in the complex plane. The second issue has to do with a chirped Manakov system. We show that if a system is chirped too much, the soliton effect disappears. While this has been known for some time experimentally, there has not yet been a theoretical result along these lines for the Manakov system. / Ph. D.