Eur. Phys. J. D (2015) 69: 108
https://doi.org/10.1140/epjd/e2015-50877-1

Regular Article

Breather interactions, higher-order rogue waves and nonlinear tunneling for a derivative nonlinear Schrödinger equation in inhomogeneous nonlinear optics and plasmas

¹ Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, P.R. China
² Research Center for Ecological Engineering and Nonlinear Science, North China Electric Power University, Beijing 102206, P.R. China
³ School of Information, Beijing Wuzi University, Beijing 101149, P.R. China
⁴ School of Renewable Energy Sources, North China Electric Power University, Beijing 102206, P.R. China

^a e-mail: wanglei2239@126.com

Received: 8 December 2014
Received in final form: 10 February 2015
Published online: 16 April 2015

Abstract

Under investigation in this paper is a variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equation governing the femtosecond pulses in the inhomogeneous optical fibers or nonlinear Alfvén waves in the inhomogeneous plasmas. Higher-order breather and rogue wave solutions of the vc-DNLS equation are obtained via the variable-coefficient modified Darboux transformation. Two types of the breather interactions (the head-on and overtaking collisions) are exhibited with different spectral parameters. By suitably choosing the inhomogeneous functions, the parabolic breather, periodic breather, breather amplification and breather evolution are demonstrated. Furthermore, the characteristics of the higher-order fundamental rogue wave, periodic rogue wave and composite rogue wave are graphically discussed. Additionally, the nonlinear tunneling of the higher-order breathers and rogue waves are studied.