# Transparent nonlinear networks

## TL;DR

This paper introduces a method for reflectionless soliton transport in networks modeled by nonlinear Schrödinger equations, using transparent boundary conditions to connect Kirchhoff conditions with transparent ones, applicable to various graph topologies.

## Contribution

It develops a framework linking Kirchhoff and transparent boundary conditions for soliton transport on metric graphs, enabling reflectionless transmission in complex network structures.

## Key findings

- Derived simple constraints for transparent boundary conditions on metric graphs.
- Demonstrated the approach on a star graph topology.
- Extended the method to more complex graph structures.

## Abstract

We consider the reflectionless transport of solitons in networks. The system is modeled in terms of the nonlinear Schr\"odinger equation on metric graphs, for which transparent boundary conditions at the branching points are imposed. This allows to derive simple constraints, which link equivalent usual Kirchhoff-type vertex conditions to the transparent ones. Our approach is applied to a metric star graph. An extension to more complicated graph topologies is straight forward.