Bilinear forms and vector bright solitons for a coupled nonlinear Schrödinger system with variable coefficients in an inhomogeneous optical fiber

Abstract

In this paper, outcomes of the study on the bilinear forms and vector bright solitons for a coupled nonlinear Schrödinger system with variable coefficients are presented, which describes the simultaneous pulse propagation of the M-field components in an inhomogeneous optical fiber, where M is a positive integer. Under the integrable condition, we derive the bilinear forms, which are different from those in the existing literatures, and obtain the bright N-soliton solutions, where N is a positive integer. When M = 3, via the asymptotic analysis, we find that the amplitudes of the bright solitons are dependent on the amplification/absorption effect, $\mathrm{\Gamma }(z)$, and the velocities of the bright solitons are related to the group velocity dispersion, $\mathrm{\Lambda }(z)$, where z represents the spatial coordinate. Head-on, overtaking and inelastic interactions, and bound states between the two solitons are presented. We extend our analysis to M fields to obtain the vector bright N-soliton solutions.

Keywords:

• Inhomogeneous optical fiber
• coupled nonlinear Schrödinger system
• bilinear forms
• bright solitons
• Kadomtsev–Petviashvili hierarchy reduction

Acknowledgments

We express our sincere thanks to the Editors and Reviewers for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Whose time duration is of the order of a picosecond (${10}^{-15}$ second) or less [1].

Additional information

Funding

This work has been supported by National Natural Science Foundation of China [grant number 11772017], [grant number 11272023], [grant number 11805020], by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC): [grant number 2017ZZ05] and by the Fundamental Research Funds for the Central Universities of China [grant number 2011BUPTYB02].