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

TL;DR

This paper models the reflectionless propagation of vector solitons in networks using the Manakov system on metric graphs with transparent boundary conditions, providing a framework for reflectionless transport in complex network topologies.

Contribution

It introduces a novel approach combining Kirchhoff and transparent boundary conditions for the Manakov system on metric graphs, enabling reflectionless soliton transport in network models.

Findings

Derived simple constraints for nonlinearity coefficients at vertices.

Extended the method from star graphs to complex topologies.

Established a framework for reflectionless vector soliton propagation.

Abstract

We consider the reflectionless transport of Manakov solitons in networks. The system is modelled 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. Although the method is used for a metric star graph, an extension to more complicated graph topologies is easily possible.