Date of Award
Master of Science (MSc)
Mathematics and Statistics
A model with nonlinear Schrödinger (NLS) equation used for describing pulse propagations in photopolymers is considered. We focus on a case in which change of refractive index is proportional to the square of amplitude of the electric field and consider 2-dimensional spatial domain. After formal derivation of the NLS approximation from the wave-Maxwell equation, we establish well-posedness and perform rigorous justification analysis to show smallness of error terms for appropriately small time intervals. We conclude by numerical simulation to illustrate the results in one-dimensional case.
Ponomarev, Dmitry, "Justification of a nonlinear Schrödinger model for polymers" (2012). Open Access Dissertations and Theses. Paper 6981.
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