Spectral continuation study of the temporally periodic solitons of the damped-driven nonlinear Schrödinger equations
Master Thesis
2012
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University of Cape Town
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Abstract
In this thesis we develop and employ a spectral continuation algorithm, implemented in AUTO, to study the temporally periodic spatially localised soliton solutions of the driven, damped nonlinear Schrödinger equations, both in the case of parametric driving and direct driving. We hope that this study is of interest not only in the context of the nonlinear Schrödinger equations but also separately as a study of an efficient numerical algorithm for continuing (path-following) solutions to general two-dimensional periodic soliton bearing PDEs.
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Reference:
Lee-Thorpe, J. 2012. Spectral continuation study of the temporally periodic solitons of the damped-driven nonlinear Schodinger equations. Masters’ Thesis. University of Cape Town.