Edge Solitons in a Nonlinear Mechanical Topological Insulator

TL;DR

This paper discovers and analyzes localized unidirectional edge solitons in a 2D mechanical topological insulator, showing their persistence due to topological protection and modeling their behavior with the nonlinear Schrödinger equation.

Contribution

It introduces the concept of edge solitons in a mechanical topological insulator and demonstrates their theoretical and numerical existence and properties.

Findings

Edge solitons are localized and unidirectional.

Topological protection ensures their persistence.

The nonlinear Schrödinger equation models their envelope dynamics.

Abstract

We report localized and unidirectional nonlinear traveling edge waves discovered theoretically and numerically in a 2D mechanical (phononic) topological insulator. The lattice consists of a collection of pendula with weak Duffing nonlinearity connected by linear springs. We show that the classical 1D nonlinear Schrodinger equation governs the envelope of 2D edge modes, and study the propagation of traveling waves and rogue waves in 1D as edge solitons in 2D. As a result of topological protection, these edge solitons persist over long time intervals and through irregular boundaries.