A Priori Bounds and Global Bifurcation Results for Frequency Combs Modeled by the Lugiato--Lefever Equation
A Priori Bounds and Global Bifurcation Results for Frequency Combs Modeled by the Lugiato--Lefever Equation
In nonlinear optics $2\pi$-periodic solutions $a\in C^2([0,2\pi];\mathbb{C})$ of the stationary Lugiato--Lefever equation $-d a''= ({\rm i} -\zeta)a +|a|^2a-{\rm i} f$ serve as a model for frequency combs, which are optical signals consisting of a superposition of modes with equally spaced frequencies. We prove that nontrivial frequency combs can only be …