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arXiv · 1810.11983

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

Zhou-Zheng Kang·Tie-Cheng Xia
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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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Zhou-Zheng Kang, Tie-Cheng Xia. 2018-10-29. Riemann-Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrodinger equation in an optical fiber. https://arxiv.org/abs/1810.11983

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