Self-trapped leaky waves in lattices: discrete and Bragg soleakons

TL;DR

This paper introduces lattice soleakons, self-trapped waves in periodic potentials, distinguishing between discrete and Bragg types, with different stability and power emission behaviors, advancing understanding of nonlinear wave localization.

Contribution

The paper predicts and characterizes two novel types of lattice soleakons supported by nonlinearities in periodic potentials, expanding the theory of self-trapped leaky waves.

Findings

Discrete soleakons propagate robustly but eventually disintegrate.

Bragg soleakons self-trap without disintegrating.

Different nonlinearities lead to distinct soleakon behaviors.

Abstract

We propose lattice soleakons: self-trapped waves that self-consistently populate leaky modes of their self-induced defects in periodic potentials. Two types, discrete and Bragg, lattice soleakons are predicted. Discrete soleakons that are supported by combination of self-focusing and self-defocusing nonlinearities propagate robustly for long propagation distances. They eventually abruptly disintegrate because they emit power to infinity at an increasing pace. In contrast, Bragg soleakons self-trap by only self-focusing, and they do not disintegrate because they emit power at a decreasing rate.