Inverse-scattering approach to femtosecond solitons in monomode optical fibers

Abstract

Using the inverse-scattering transform with 3×3 U-V matrix representation and fully exploiting the symmetry properties of the scattering matrix elements, we found the one-parameter single-soliton, the four-parameter breather soliton, and the general N-soliton solutions of a perturbed nonlinear Schrödinger equation which describes the femtosecond pulse propagation in optical fibers. The threshold power below which the one-parameter single soliton cannot be formed was given. The main characteristic of the general single-soliton solution of the perturbed nonlinear Schrödinger equation is that it presents an arbitrary number of ‘‘humps’’ (local maxima of the amplitude) of different heights.Peer ReviewedPostprint (published version

Rogue waves of the Sasa-Satsuma equation in a chaotic wave field

“…There is a number of publications dealing with the solutions of the SSE [33][34][35][36][37][38][39]. The form of Eq.…”

“…The form of Eq. (1) has been used in a series of works by Mihalache et al [33][34][35]. The form of the SSE in the work by Wright III [36] is slightly different from the original version:…”

Applications of a Generalized Extended (G'/G) -Expansion Method to Find Exact Solutions of Two Nonlinear Schrödinger Equations with Variable Coefficients

“…The propagation of the optical solitons is usually governed by the nonlinear Schrödinger equation (NLSE), which is one of the most important models in modern nonlinear science. Moreover, much attention has been paid to the investigation on the generalized NLSEs with constant coecients as a kind of ideal models of the much more complicated physical problems [6,7]. As a matter of fact, in a real ber there exist some ber nonuniformities to inuence various eects such as the gain or loss, GVD and SPM, etc.…”

Anti-dark and Mexican-hat solitons in the Sasa-Satsuma equation on the continuous wave background

“…Under the vanishing boundary condition (VBC), Eq. (2) with σ = 1 possesses the common single-hump soliton [5,15], the double-hump soliton behaving like two in-phase solitons with a fixed separation [5,6], and the multi-hump breather with the periodically-oscillating structure [6,7]. Under the nonvanishing boundary condition, Eq.…”

“…Up to now, many integrable properties of Eq. (2) have been detailed, like the inverse scattering transform scheme [5,6], bilinear representation [7], Painlevé property [8], conservation laws [9], nonlocal symmetries [10], squared eigenfunctions [11], Bäcklund transformation [12] and Darboux transformation (DT) [13,14].…”