Soliton dynamics in finite nonlocal media with cylindrical symmetry

TL;DR

This paper investigates how finite boundaries influence the behavior of spatial nonlocal solitons in cylindrically symmetric media, deriving analytical expressions and revealing boundary-induced bifurcations affecting soliton dynamics.

Contribution

It introduces an analytical approach combining Ehrenfest's theorem and Green's function to analyze boundary effects on nonlocal solitons, highlighting boundary conditions' role in bifurcation phenomena.

Findings

Boundary conditions significantly affect soliton dynamics.

A supercritical pitchfork bifurcation occurs at a threshold boundary condition.

Analytical expressions accurately predict boundary-induced forces on solitons.

Abstract

The effect of finite boundaries in the propagation of spatial nonlocal solitons in media with cylindrical symmetry is analyzed. Using Ehrenfest's theorem together with the Green's function of the nonlinear refractive index equation, we derive an analytical expression for the force exerted on the soliton by the boundaries, verifying its validity by full numerical propagation. We show that the dynamics of the soliton are determined not only by the degree of nonlocality, but also by the boundary conditions for the refractive index. In particular, we report that a supercritical pitchfork bifurcation appears when the boundary condition exceed a certain threshold value.