Eur. Phys. J. Plus (2017) 132: 488
https://doi.org/10.1140/epjp/i2017-11780-5

Regular Article

Solitons and breather-to-soliton transitions for an integrable higher-order variable-coefficient nonlinear Schrödinger equation in an optical fiber

State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China

^* e-mail: tian_bupt@163.com

Received: 20 August 2017
Accepted: 20 October 2017
Published online: 27 November 2017

Abstract

Under investigation in this paper is an integrable eighth-order variable-coefficient nonlinear Schrödinger equation in an optical fiber. One-, two-, three-soliton and the first-, second-order breather solutions are obtained via the Darboux transformation. Properties of the solitons are discussed graphically. Breather-to-soliton transitions are studied under certain constraints. Discussions indicate that the soliton amplitude is not related to the variable coefficients, but related to some spectral parameters, while the soliton velocity is related to both the variable coefficients and spectral parameters. We find that there are two types of the breather-to-soliton transitions, M-shaped and W-shaped, which are determined through the spectral parameters.