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arXiv · 1809.07035

Riemann-Hilbert method and soliton solutions in the system of two-component Hirota equations

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

In this letter we examine the two-component Hirota (TH) equations which describes the pulse propagation in a coupled fiber with higher-order dispersion and self-steepening. As the TH equations is a complete integrable system, which admits a $3\times 3$ Ablowitz-Kaup-Newell-Segu(AKNS)-type Lax pair, we obtain the general N-soliton solutions of the TH equations via the Riemann-Hilbert(RH) method when the jump matrix of a specific RH problem is a $3\times3$ unit matrix. As an example, the expression of one- and two-soliton are displayed explicitly.

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Fang Fang, Beibei Hu, Ling Zhang, Ning Zhang. 2018-09-19. Riemann-Hilbert method and soliton solutions in the system of two-component Hirota equations. https://arxiv.org/abs/1809.07035

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