Solitons in nonlocal nonlinear media: Exact solutions

Abstract

We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties of these solitons and show their stability.

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

“…It has been shown recently that the one-dimensional version of Eq. (2) with nonlinearity (4) supports propagation of stable bright and dark solitons [17]. Another limiting case, the so-called highly nonlocal limit, refers to the situation when the nonlocal response function is much wider than the beam itself [see Fig.1(d)].…”

Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality

“…The so-called weakly nonlocal limit (σ 1) also presents a simpler model, which can be solved exactly for both dark and bright solitons [35].…”

Route to Nonlocality and Observation of Accessible Solitons

“…[6,7]); spatially nonlocal effects have been associated to photorefractive [8,9,10,11] and thermal or diffusive responses [12,13]. To assess the role of nonlocality, theoretical studies tend to distinguish between highly and weakly nonlocal behaviors [14,15,16], by comparing the spatial extent of the material response (the so-called kernel-function) and the optical beam waist. Specific kernel functions, however, strongly depend on the physical system and, as in the case of BEC, [5] they are hard to determine and apply to experimental results.…”