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|Title:||Justification of a nonlinear Schrödinger model for polymers|
|Department:||Mathematics and Statistics|
|Keywords:||justification analysis;photopolymers;NLS equation;wave-Maxwell system;Optics;Partial Differential Equations;Polymer Chemistry;Optics|
|Abstract:||<p>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.</p>|
|Appears in Collections:||Open Access Dissertations and Theses|
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