Solitons in a chain of PT-invariant dimers

TL;DR

This paper explores the behavior of solitons in a chain of PT-invariant nonlinear dimers, revealing their mobility, stability thresholds, and differences from traditional DNLS lattices, with implications for nonlinear wave dynamics.

Contribution

It demonstrates the connection between PT-symmetric dimer solitons and DNLS solitons, deriving approximate solutions and analyzing stability and mobility properties.

Findings

Large-width solitons are mobile with nearly elastic collisions.

Narrow solitons are pinned and numerically constructed from the anti-continuum limit.

High-amplitude solitons become unstable and blow up, with the threshold decreasing as gain-loss increases.

Abstract

Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrodinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anti-continuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear PT-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability threshold drops with the increase of the gain-loss coefficient, but it does not depend on the lattice coupling constant, nor on the soliton's velocity.