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arXiv · 1809.09472

Riemann-Hilbert approach for a mixed coupled nonlinear Schr\"odinger system and its soliton solutions

Fang Fang·Beibei Hu·Ling Zhang·Ning Zhang
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Abstract

In this work, we examine the integrable mixed coupled nonlinear Schr\"odinger (mCNLS) system, which describe the propagation of an optical pulse in a birefringent optical fiber. By the Riemann-Hilbert(RH) approach, the N-soliton solutions of the mCNLS system can be expressed explicitly when the jump matrix of a specific RH problem is a $3\times3$ unit matrix. As a special example, the expression of one- and two-soliton are displayed explicitly. More generally, as a promotion, an integrable generalized multi-component NLS system with its linear spectral problem be discussed. It is hoped that our results can help enrich the nonlinear dynamical behaviors of the mCNLS.

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Fang Fang, Beibei Hu, Ling Zhang, Ning Zhang. 2018-09-22. Riemann-Hilbert approach for a mixed coupled nonlinear Schr\"odinger system and its soliton solutions. https://arxiv.org/abs/1809.09472

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