Particle and wave dynamics of nonlocal solitons in external potentials

TL;DR

This paper investigates the dynamics of nonlocal bright solitons in external potentials, deriving analytical solutions and identifying regimes of trapping, reflection, and transmission, supported by numerical simulations.

Contribution

It introduces analytical models for nonlocal soliton behavior in external potentials, including delta-like defects, and characterizes different dynamical regimes.

Findings

Solitons behave like Newtonian particles in slowly varying potentials.

Identification of trapping, reflection, and transmission regimes at point defects.

Analytical solutions are validated by numerical simulations.

Abstract

We study nonlocal bright solitons subject to external spatially nonuniform potentials. If the potential is slowly varying on the soliton scale, we derive analytical soliton solutions behaving like Newtonian particles. If the potential has the form of an attractive delta-like point defect, we identify different dynamical regimes, defined by the relative strength of the nonlocality and the point defect. In these regimes, the soliton can be trapped at the defect's location, via a nonlinear resonance with a defect mode -- which is found analytically -- reflected by or transmitted through the defect, featuring a wave behavior. Our analytical predictions are corroborated by results of direct numerical simulations.