Publisher's Note:N-order bright and dark rogue waves in a resonant erbium-doped fiber system [Phys. Rev. E86, 066603 (2012)]

Abstract

The rogue waves in a resonant erbium-doped fibre system governed by a coupled system of the nonlinear Schrödinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the breather solutions of the normalized slowly varying amplitude of the complex field envelope E, polarization p and population inversion η. The norder breather solutions of the three fields are constructed using Darboux transformation (DT) by assuming periodic seed solutions. What is more, the n-order rogue waves are given by determinant forms with n + 3 free parameters. Furthermore, the possible connection between our rouge waves and the generation of supercontinuum generation is discussed.

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

“…The RWs have also been observed experimentally in physical systems such as water wave tank [22], capillary waves [23] and nonlinear optics [5,24]. Several theoretical studies on the dynamics of RWs in nonlinear fiber optics [25,26], plasma physics [27], laser-plasma interactions [28], and even econophysics [29], described by scalar NLS equation, have been made in recent times. Now, as mentioned in the beginning, the dynamics of a cigar shaped BEC at absolute zero temperature is usually described by the mean-field GP equation (1), which is a generalized form of the ubiquitous constant coefficient NLS equation (2), for the wave function of the condensate.…”

Rogue-wave interaction of the generalized variable-coefficient Hirota–Maxwell–Bloch system in fiber optics

“…Lax pairs and Painlevé property [1], multi-soliton solutions and Darboux transformation (DT) [13], roguewave solutions and generalized DT [14] for System (1) have been obtained. With respect to System (1), nonlinear tunneling of the nonautonomous optical solitons [15] and propagation of the ultrashort pulses along a nonlinear light guide containing resonant impurities [12] have been attained; The solitons described by System (1) have been experimentally exhibited [16].…”

Multi-Soliton and Rational Solutions for the Extended Fifth-Order KdV Equation in Fluids

“…Among these approaches, the DT can be employed to construct the soliton solutions for NLEEs through an algebraically iterative algorithm [20][21][22][23][24][25][26][27][28][29][30]. However, the elementary DT cannot be applicable directly to construct the rational solutions for NLEEs [25][26][27][28][29][30].…”