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On the Riemann-Hilbert problem for the integrable three-coupled Hirota system with a 4×4 matrix Lax pair

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  • Hu, Beibei
  • Lin, Ji
  • Zhang, Ling

Abstract

In this work, we will investigate a complete integrable variable coefficient three-coupled Hirota system, which possesses a generalization of fourth-order matrix spectral problem AKNS type Lax pair. With the help of the unified transform method, the initial-boundary value problems (IBVPs) of the three-coupled Hirota equation on the half-line will be discussed. In other words, one can obtain the solutions of the three-coupled Hirota equation by solving a fourth-order matrix Riemann-Hilbert problem in the complex ξ-plane. Furthermore, we will show that three spectral functions φ(ξ),ϕ(ξ) and ψ(ξ) are not independent but meet a key relationship, i.e. the so-called global relation.

Suggested Citation

  • Hu, Beibei & Lin, Ji & Zhang, Ling, 2022. "On the Riemann-Hilbert problem for the integrable three-coupled Hirota system with a 4×4 matrix Lax pair," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    • Handle: RePEc:eee:apmaco:v:428:y:2022:i:c:s0096300322002764
    DOI: 10.1016/j.amc.2022.127202
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    References listed on IDEAS

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    1. Hu, Beibei & Zhang, Ling & Xia, Tiecheng & Zhang, Ning, 2020. "On the Riemann-Hilbert problem of the Kundu equation," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    2. Hu, Bei-Bei & Xia, Tie-Cheng & Ma, Wen-Xiu, 2018. "Riemann–Hilbert approach for an initial-boundary value problem of the two-component modified Korteweg-de Vries equation on the half-line," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 148-159.
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