Eur. Phys. J. Plus (2018) 133: 96
https://doi.org/10.1140/epjp/i2018-11931-2

Regular Article

Integrability and solitons for the higher-order nonlinear Schrödinger equation with space-dependent coefficients in an optical fiber

Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, 100191, Beijing, China

^* e-mail: gaoyt163@163.com

Received: 12 December 2017
Accepted: 23 January 2018
Published online: 8 March 2018

Abstract

Under investigation in this paper is a higher-order nonlinear Schrödinger equation with space-dependent coefficients, related to an optical fiber. Based on the self-similarity transformation and Hirota method, related to the integrability, the N-th-order bright and dark soliton solutions are derived under certain constraints. It is revealed that the velocities and trajectories of the solitons are both affected by the coefficient of the sixth-order dispersion term while the amplitudes of the solitons are determined by the gain function. Amplitudes increase when the gain function is positive and decrease when the gain function is negative. Furthermore, we find that the intensities of dark solitons are presented as a superposition of the solitons and stationary waves.