Eur. Phys. J. D (2015) 69: 214
https://doi.org/10.1140/epjd/e2015-60316-0

Regular Article

Nonautonomous characteristics of the breathers and rogue waves for a amplifier nonlinear Schrödinger Maxwell-Bloch system

¹ Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, P.R. China
² School of Electrical and Electronic Engineering, North China Electric Power University, Beijing 102206, P.R. China
³ School of Information, Beijing Wuzi University, Beijing 101149, P.R. China

^a e-mail: wanglei2239@126.com

Received: 29 May 2015
Received in final form: 20 July 2015
Published online: 17 September 2015

Abstract

Under investigation in this paper is a amplifier nonlinear Schrödinger Maxwell-Bloch (NLS-MB) system which describes the propagation of optical pulses in an inhomogeneous erbium doped fiber. Nonautonomous breather and rogue wave (RW) solutions of the amplifier NLS-MB system are constructed via the modified Darboux transformation with the inhomogeneous parameters. By suitably choosing the dispersion coefficient function, several types of inhomogeneous nonlinear waves are obtained in: (1) periodically fluctuating dispersion profile; (2) exponentially increasing (or decreasing) dispersion profile; and (3) linearly decreasing (increasing) dispersion profile. The nonautonomous characteristics of the breathers and RWs are graphically investigated, including the breather accelerating and decelerating motions, boomerang breather, breather compression, breather evolution, periodic RW, boomerang RW and stationary RW. Such novel patterns as the periodic breathers and rogue-wave fission of the amplifier NLS-MB system are exhibited by properly adjusting the group velocity dispersion function and interaction parameter between silica and doped atoms.