Bifurcation structure of dissipative solitons
Numerical bifurcation analysis of reversible system of ordinary differential equations describing stationary solutions in a model of optical cavity with external injection is performed. Two cases are considered: (i) Kerr nonlinearity when the cavity can be described by the driven-damped nonlinear Schrödinger equation (NSE) and (ii) purely dissipative nonlinearity introduced by intracavity saturable absorber. Special attention is given to fronts and localized structures corresponding to heteroclinic connections which result from intersections between the invariant manifolds of different patterned and homogeneous stationary solutions of the full PDE model. The relation between the observed phenomena and those taking place near a degenerate Hamiltonian-Hopf bifurcation is discussed.
homoclinic and heteroclinic bifurcations
scientific article; zbMATH DE number 5142359