Eur. Phys. J. Plus (2017) 132: 512
https://doi.org/10.1140/epjp/i2017-11781-4

Regular Article

Solitons, breather and bound waves for a generalized higher-order nonlinear Schrödinger equation in an optical fiber or a planar waveguide

School of Computer Information Management, Inner Mongolia University of Finance and Economics, 010070, Hohhot, China

^* e-mail: zhongzhou-lan@buaa.edu.cn

Received: 20 October 2017
Accepted: 7 November 2017
Published online: 8 December 2017

Abstract

In this paper, a generalized higher-order nonlinear Schrödinger equation with variable coefficients is investigated, which could describe the attosecond pulses in an optical fiber or a continuous wave beam in a planar waveguide. Based on the transformation, symbolic computation and Hirota method, the new bilinear forms, one-, two-, three-soliton solutions are obtained under certain constraints. We see that: i) the fifth-order dispersion may affect the soliton velocity as well as the velocities of the breathers and bound solitons; ii) the fifth-order dispersion may influence the shapes of the breathers and bound solitons; iii) the gain function has an impact on the intensities of the solitons, breathers and bound solitons; iv) the gain function may change the breathers’ and bound solitons’ periods and v) the solitons can change into the breathers under the influence of a certain gain function.