Multibreather solitons in the diffraction managed NLS equation

We study analytically and numerically localized breather solutions in the averaged discrete nonlinear Schrödinger equation (NLS) with diffraction management, a system that models coupled waveguide arrays with periodic diffraction management geometries. Localized breathers can be characterized as constrained critical points of the Hamiltonian of the averaged diffraction managed NLS. In addition to local extrema, we find numerically more general solutions that are saddle points of the constrained Hamiltonian. An interesting class of saddle points are “multi-bump” solutions that are close to superpositions of translates of simpler breathers. In the case of zero residual diffraction and small diffraction management, the existence of multibumps can be shown rigorously by a continuation argument.