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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus


IMPACT FACTOR 2016: 1.432

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 0.403
Source Normalized Impact per Paper (SNIP) 2017: 0.632

Online
ISSN
1865-7109
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Volume 74, Issue 2

Issues

Riemann–Hilbert Problem and Multi-Soliton Solutions of the Integrable Spin-1 Gross–Pitaevskii Equations

Xiu-Bin Wang / Bo Han
Published Online: 2018-10-26 | DOI: https://doi.org/10.1515/zna-2018-0387

Abstract

Under investigation in this article is the integrable spin-1 Gross–Pitaevskii (SGP) equations, which can be used to describe light transmission in bimodal nonlinear optical fibres. The spectral analysis with 4 × 4 Lax pairs is performed for the integrable SGP equations, from which a Riemann Hilbert problem is formulated. Furthermore, N-soliton solutions of this integrable SGP equations are expressed in terms of solutions of the Riemann–Hilbert problem by using the Plemelj formulae. Finally, collision dynamics between two solitons is also analyzed. Our results can be used to enrich and explain some related nonlinear phenomena.

Keywords: Integrable Spin-1 Gross–Pitaevskii (SGP) Equations; Inverse Scattering Transform; Riemann–Hilbert Problem (RHP); Soliton Solution

PACS: 05.45.Yv; 02.30.Jr; 02.30.Ik; 04.20.Jb

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About the article

Received: 2018-08-10

Accepted: 2018-10-11

Published Online: 2018-10-26

Published in Print: 2019-01-28


Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11871180

We express our sincere thanks to the editor and reviewers for their valuable comments. This work is supported by the National Natural Science Foundation of China (Grant No. 11871180).


Citation Information: Zeitschrift für Naturforschung A, Volume 74, Issue 2, Pages 139–145, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2018-0387.

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