Ring dark and anti-dark solitons in nonlocal media

TL;DR

This paper reports the discovery and analysis of ring dark and anti-dark solitons in nonlocal media, demonstrating their analytical solutions, stability, and collision behavior, with potential implications for nonlinear wave dynamics.

Contribution

It introduces explicit analytical solutions for ring dark and anti-dark solitons in nonlocal media and analyzes their stability and collision properties.

Findings

Solitons satisfy an effective cylindrical Kadomtsev-Petviashvilli equation.

They propagate undistorted and undergo quasi-elastic collisions.

Solutions are expressed in closed form, confirming their stability.

Abstract

Ring dark and anti-dark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable continuous-wave background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvilli (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties.