Colloquium: Bifurcation theories for a model from nonlinear optics, Mariana Haragus (Université de Franche-Comté)
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We consider the Lugiato-Lefever equation, which is a nonlinear Schrödinger-type equation with damping, detuning and driving, derived in nonlinear optics by Lugiato and Lefever (1987). While intensively studied in the physics literature, there are relatively few rigorous mathematical studies of this equation. Of particular interest for the physical problem, is the dynamical behavior of periodic and localized steady waves. The underlying mathematical questions concern the existence and the stability of these types of waves. In this talk, I'll show how different tools from bifurcation theory can be used in the analysis of these questions. The focus will be on periodic waves and their stability.