title: Class of compound dissipative solitons as a result of collisions in one and two spatial dimensions.
abstract: We study the interaction of quasi-one-dimensional (quasi-1D) dissipative solitons (DSs). Starting with quasi-1D solutions of the cubic-quintic complex Ginzburg-Landau (CGL) equation in their temporally asymptotic state as the initial condition, we find, as a function of the approach velocity and the real part of the cubic interaction of the two counterpropagating envelopes: interpenetration, one compound state made of both envelopes or two compound states. For the latter class both envelopes show DSs superposed at two different locations. The stability of this class of compound states is traced back to the quasilinear growth rate associated with the coupled system. We show that this mechanism also works for 1D coupled cubic-quintic CGL equations. For quasi-1D states that are not in their asymptotic state before the collision, a breakup along the crest can be observed, leading to nonunique results after the collision of quasi-1D states.
authors.affiliation: Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Avenida Monseñor Álvaro del Portillo 12.455, Las Condes, Santiago, Chile and Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany.
authors.forename: Orazio
authors.initials: O
authors.lastname: Descalzi
authors.affiliation: Department of Physics, University of Bayreuth, 95440 Bayreuth, Germany.
authors.forename: Helmut R
authors.initials: HR
authors.lastname: Brand
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical; D009038:Motion