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On the Riemann-Hilbert problem of the Kundu equation

Author

Listed:
  • Hu, Beibei
  • Zhang, Ling
  • Xia, Tiecheng
  • Zhang, Ning

Abstract

The Kundu equation as a special case of the complex Ginzburg–Landau equation can be used to describe a slice of phenomena in physics and mechanics. In this paper, we analyzed the Kundu equation on the half-line by the Fokas method and proved that the potential function u(z, t) of the Kundu equation can be uniquely expressed by the solution of Riemann-Hilbert (RH) problem. It also includes the RH problem of the derivative nonlinear Schrödinger equation (also known as Kaup-Newell equation) (if ε=0), Chen–Lee–Liu equation (if ε=14) and Gerjikov–Ivanov equation (if ε=12) on the half-line.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:381:y:2020:i:c:s0096300320302319
    DOI: 10.1016/j.amc.2020.125262
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    References listed on IDEAS

    as
    1. Yating Yi & Zhengrong Liu, 2013. "The Bifurcations of Traveling Wave Solutions of the Kundu Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, October.
    2. Shaoyong Li & Zhengrong Liu, 2013. "The Traveling Wave Solutions and Their Bifurcations for the BBM-Like Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-17, August.
    3. 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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    Cited by:

    1. 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).

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