Fundamental solitons in discrete lattices with a delayed nonlinear response

TL;DR

This paper investigates how delayed nonlinear responses affect the stability and dynamics of fundamental solitons in discrete lattices, revealing conditions for stability, instability, and resulting behaviors like breathers or decay patterns.

Contribution

It introduces the impact of finite relaxation time on discrete soliton stability and dynamics, highlighting the transition from stable to unstable regimes based on nonlinearity response speed.

Findings

On-site solitons are stable in rapidly responding media.

Slow relaxation leads to soliton instability and decay.

Stable solitons can move freely across the lattice.

Abstract

The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are stable, and their broad inter-site counterparts are marginally stable, featuring a virtually vanishing real instability eigenvalue. The solitons become unstable in the case of the slowly relaxing nonlinearity. The character of the instability alters with the increase of the delay time, which leads to a change in the dynamics of unstable discrete solitons. They form robust localized breathers in rapidly relaxing media, and decay into oscillatory diffractive pattern in the lattices with a slow nonlinear response. Marginally stable solitons can freely move across the lattice.