# Honors College Thesis

## Qualitative Analysis of Maxwell-Duffing Models in Nonlinear Optics Public Deposited

https://ir.library.oregonstate.edu/concern/honors_college_theses/hq37vt94s

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• In this thesis we analyze a model for Kerr optical materials consisting of Maxwell's equations along with the dispersive Duffing model. We consider Duffing models with cubic and quintic polynomial nonlinearities. We assume a traveling wave solution to this nonlinear electromagnetic system and analyze it using the theory of dynamical systems. A bifurcation analysis is conducted that depends on parameters $\alpha$, the Kerr nonlinearity coefficient, $\Gamma$, the damping term, and $v$, the velocity of the traveling wave. We predict saddles and unstable nodes and spirals when we have damping, i.e., $\Gamma\neq0$, and saddles and centers when $\Gamma=0$ and the system is conservative.
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