Manakov system on metric graphs: Modeling the reflectionless propagation of vector solitons in networks

Abstract

We consider the reflectionless transport of Manakov solitons in networks. The system is modeled in terms of the Manakov system on metric graphs subject to transparent boundary conditions at the branching points. Simple constraints combining the equivalent usual Kirchhoff vertex conditions with the transparent conditions are derived in terms of nonlinearity coefficients. Formulation of the problem, derivation of transparent boundary conditions and numerical experiment showing absence of the back scattering in the transmission of soliton through the vertex under the above constraints are presented for the case of metric star graph. Extension of the problem to other graph topologies is briefly discussed by considering the metric tree graph.