# Topological edge states and gap solitons in the nonlinear Dirac model

## TL;DR

This paper investigates topological edge states and gap solitons in nonlinear Dirac models, revealing their interactions and tunability in one- and two-dimensional topological photonic systems through analytical and numerical methods.

## Contribution

It provides the first detailed analysis of the interaction between topological edge states and gap solitons in nonlinear Dirac systems, including analytical solutions and numerical modeling.

## Key findings

- Strong nonlinear interaction between edge states and gap solitons.
- Analytical solutions demonstrate nonlinear tunability of localized states.
- Numerical simulations confirm wave transport behaviors in topological systems.

## Abstract

Topological photonics has emerged recently as a novel approach for realizing robust optical circuitry, and the study of nonlinear effects in topological photonics is expected to open the door for tunability of photonic structures with topological properties. Here, we study the topological edge states and topological gap solitons which reside in the same bandgaps described by the nonlinear Dirac model, in both one- and two-dimensions. We reveal strong nonlinear interaction between those dissimilar topological modes manifested in the excitation of the topological edge states by scattered gap solitons. Nonlinear tunability of localized states is explicated with exact analytical solutions for the two-component spinor wave function. Our studies are complemented by spatiotemporal numerical modeling of the wave transport in one- and two-dimensional topological systems.