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

2018/09/19 by Fang Fang, Fang, Fang, Beibei Hu +5
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1809.07035

openalex publication_date 2018/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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× 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 3×3 unit matrix. As an example, the expression of one- and two-soliton are displayed explicitly.

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