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

2018/10/29 by Kang, Zhou-Zheng, Xia, Tie-Cheng
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1810.11983

Abstract

This paper aims to present an application of Riemann-Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrodinger equation arising in an optical fiber. Starting from the spectral analysis of the Lax pair, a Riemann-Hilbert problem is formulated. Then by solving the obtained Riemann-Hilbert problem under the reflectionless case, N-soliton solution is generated for the eighth-order nonlinear Schrodinger equation. Finally, the three-dimensional plots and two-dimensional curves with specific choices of the involved parameters are made to show the localized structures and dynamic behaviors of one- and two-soliton solutions.

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