title: Non-unique results of collisions of quasi-one-dimensional dissipative solitons.
abstract: We investigate collisions of quasi-one-dimensional dissipative solitons (DSs) for a large class of initial conditions, which are not temporally asymptotic quasi-one-dimensional DSs. For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counter-propagating DSs, we find non-unique results for the outcome of collisions. We demonstrate that these non-unique results are intrinsically related to a modulation instability along the crest of the quasi-one-dimensional objects. As a model, we use coupled cubic-quintic complex Ginzburg-Landau equations. Among the final results found are stationary and oscillatory compound states as well as more complex assemblies consisting of quasi-one-dimensional and localized states. We analyse to what extent the final results can be described by the solutions of one cubic-quintic complex Ginzburg-Landau equation with effective parameters.
authors.affiliation: Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Mons. Álvaro del Portillo 12.455, Las Condes, Santiago, Chile Department of Physics, University of Bayreuth, Bayreuth 95440, Germany odescalzi@miuandes.cl.
authors.forename: Orazio
authors.initials: O
authors.lastname: Descalzi
authors.affiliation: Department of Physics, University of Bayreuth, Bayreuth 95440, Germany.
authors.forename: Helmut R
authors.initials: HR
authors.lastname: Brand
keywords: complex Ginzburg–Landau equation; dissipative solitons; localized structures