Riemann–Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrödinger equation in an optical fiber

This paper aims to present an application of the Riemann–Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrödinger equation arising in an optical fiber. Starting from the spectral analysis of the Lax pair, a matrix Riemann–Hilbert problem is...

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Bibliographic Details
Published in:Advances in difference equations 2019-05, Vol.2019 (1), p.1-14, Article 188
Main Authors: Kang, Zhou-Zheng, Xia, Tie-Cheng, Ma, Wen-Xiu
Format: Article
Language:English
Subjects:
Analysis
Difference and Functional Equations
Eighth-order nonlinear Schrödinger equation
Functional Analysis
Mathematics
Mathematics and Statistics
Nonlinear differential equations
Optical fibers
Ordinary Differential Equations
Partial Differential Equations
Propagation
Riemann–Hilbert approach
Schrodinger equation
Soliton solutions
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Summary:This paper aims to present an application of the Riemann–Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrödinger equation arising in an optical fiber. Starting from the spectral analysis of the Lax pair, a matrix Riemann–Hilbert problem is formulated strictly. Then, by solving the obtained Riemann–Hilbert problem under the reflectionless case, N -soliton solution is generated for the eighth-order nonlinear Schrödinger equation. Finally, the localized structures and dynamic behaviors of one- and two-soliton solutions are illustrated by some figures.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2121-5