# Dynamics of Dirac solitons in networks

## TL;DR

This paper investigates the behavior of Dirac solitons in network structures modeled by the nonlinear Dirac equation, revealing conditions for reflectionless transmission at network junctions through analytical and numerical methods.

## Contribution

It derives conditions for reflectionless Dirac soliton transmission in network models and confirms these findings with numerical simulations.

## Key findings

- Reflectionless vertex transmission of Dirac solitons under specific conditions
- Analytical constraints on nonlinearity coefficients for reflectionless transmission
- Numerical simulations validating analytical results

## Abstract

We study dynamics of Dirac solitons in prototypical networks modeling them by the nonlinear Dirac equation on metric graphs. Soliton solutions of the nonlinear Dirac equation on simple metric graphs are obtained. It is shown that these solutions provide reflectionless vertex transmission of the Dirac solitons under suitable conditions. The constraints for bond nonlinearity coefficients, allowing reflectionless transmission over a Y-junction are derived. The analytical results are confirmed by direct numerical simulations.