| Contents |
| The Lugiato-Lefever equation is a cubic nonlinear Schr{\"o}dinger equation
with damping, detuning and driving force arising as a model in nonlinear
optics. We focus on the existence of steady waves which are found as
solutions of a four-dimensional reversible dynamical system in which the
evolutionary variable is the space variable. Relying upon tools from
bifurcation theory and normal forms theory, we classify the local
bifurcations and then discuss the codimension 1 bifurcations. We show
the existence of various types of steady solutions, including spatially
localized, periodic, or quasi-periodic solutions. |
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