Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation

Abstract

A theory of optical pulse propagation in cascaded transmission systems that are based on the dispersioncompensating fiber technique is developed. The existence of two scales associated with fiber dispersion and system residual dispersion leads to a simple model for the averaged pulse dynamics. In the particular case of practical importance, the averaged pulse dynamics is governed by the nonlinear Schrödinger equation. The pulse transmission stability is examined.

Compacton matter waves in binary Bose gases under strong nonlinear management

“…Substituting this ansatz in Eqs. (20,21) we obtain the corresponding condition for the compacton existence as…”

“…Existence of such solutions follows from the general stationary Eqs. (20,21) by letting A n0 = a, B n0 = b, and A n = 0, B n = c for n = n 0 . In this case one finds that exact solutions exist if chemical potentials and parameters a, b, c of the B-D compacton are related by the following equations …”

“…Moreover, they were used to induce long lived Bloch oscillations [14][15][16], dynamical localization [17], Rabi oscillations [18] of BEC gap solitons in optical lattices, Faraday waves [19,20] etc. Nonlinear management techniques were considered also in nonlinear optics to stabilize 2D and 3D solitons and to reduce collapse in optically layered media with self-focusing interaction [9], to improve communication capacities via soliton dispersion management in optical fibers [21], to create linear superpositions of gap solitons in periodic Kerr media [22], etc.…”

Averaging for Solitons with Nonlinearity Management

“…When D = D(t), the NLS equation (1) describes the dispersion management (DM) scheme in fiber optics, which is based on periodic alternation of fibers with opposite signs of the group-velocity dispersion. The DM scheme supports robust breathing solitons [4], which are well described through the averaging method by the integral NLS equation [5]. Extensions of the averaging method were developed for strong management with large variations of the dispersion coefficient [6] and for weak management with small variations of the dispersion coefficient [7].…”

“…Given the importance in nonlinear optics and condensed matter physics, of applications of the NLS equation (1) with periodically varying nonlinearity coefficient, we extend the averaging method of [5,6] to solitons with strong nonlinearity management, when the periodic variations of the nonlinearity coefficient are large in amplitude. Comparing with earlier works, we note that the averaged equation for strong dispersion management in [5,6] is nonlocal, whereas our main averaged equation (see Eq.…”