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

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arxiv 1809.07035 v1 pith:LOIY3PPC submitted 2018-09-19 math.AP

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

Fang Fang , Beibei Hu , Ling Zhang , Ning Zhang This is my paper
classification math.AP
keywords equationshirotamatrixmethodriemann-hilbertsolutionssystemtwo-component
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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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