title: Computationally determined existence and stability of transverse structures. I. Periodic optical patterns.
abstract: We present a Fourier-transform based, computer-assisted, technique to find the stationary solutions of a model describing a saturable absorber in a driven optical cavity. We illustrate the method by finding essentially exact hexagonal and roll solutions as a function of wave number and of the input pump. The method, which is widely applicable, also allows the determination of the domain of stability (Busse balloon) of the pattern, and sheds light on the mechanisms responsible for any instability. To show the usefulness of our numerical technique, we describe cracking and shrinking patches of patterns in a particular region of parameter space.
authors.affiliation: Department of Physics, University of Strathclyde, 107 Rottenrow, Glasgow G4 ONG, Scotland.
authors.forename: G K
authors.initials: GK
authors.lastname: Harkness
authors.forename: W J
authors.initials: WJ
authors.lastname: Firth
authors.forename: G-L
authors.initials: GL
authors.lastname: Oppo
authors.forename: J M
authors.initials: JM
authors.lastname: McSloy