Dragging two-dimensional discrete solitons by moving linear defects

TL;DR

This paper investigates the controlled movement of small-amplitude 2D discrete solitons attached to moving defects in a lattice, demonstrating near-lossless dragging below a critical velocity and exploring collision-induced symmetry breaking.

Contribution

It introduces a method to drag 2D discrete solitons with moving defects over long distances with minimal loss, and analyzes collision effects leading to symmetry breaking.

Findings

Dragged solitons can be moved indefinitely with minimal loss below a critical velocity.

Free solitons become pinned after transient motion, unlike defect-attached solitons.

Collisions can cause fusion and symmetry breaking of solitons.

Abstract

We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear-Schr\"{o}dinger (DNLS) lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in the uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a localized mode pinned by the Peierls-Nabarro potential, irrespective of the initial velocity. However, the soliton attached to the moving defect can be dragged over an indefinitely long distance (including routes with abrupt turns and circular trajectories) virtually without losses, provided that the dragging velocity is smaller than a certain critical value. Collisions between solitons dragged by two defects in opposite directions are studied too. If the velocity is small enough, the collision leads to a spontaneous symmetry breaking, featuring fusion of two solitons into a single one, which remains attached to either of the two defects.