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Riemann–Hilbert Problems and Soliton Solutions of Type ( λ ∗ , − λ ∗ ) Reduced Nonlocal Integrable mKdV Hierarchies

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  • Wen-Xiu Ma

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
    Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA
    School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa)

Abstract

Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the matrix Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems. One reduction is local, which replaces the spectral parameter λ with its complex conjugate λ ∗ , and the other one is nonlocal, which replaces the spectral parameter λ with its negative complex conjugate − λ ∗ . Riemann–Hilbert problems and thus inverse scattering transforms are formulated from the reduced matrix spectral problems. In view of the specific distribution of eigenvalues and adjoint eigenvalues, soliton solutions are constructed from the reflectionless Riemann–Hilbert problems.

Suggested Citation

  • Wen-Xiu Ma, 2022. "Riemann–Hilbert Problems and Soliton Solutions of Type ( λ ∗ , − λ ∗ ) Reduced Nonlocal Integrable mKdV Hierarchies," Mathematics, MDPI, vol. 10(6), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:870-:d:767362
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    References listed on IDEAS

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    1. Ma, Wen-Xiu, 2021. "N-soliton solution and the Hirota condition of a (2+1)-dimensional combined equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 270-279.
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    Cited by:

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    3. Acharya, S.P. & Janaki, M.S., 2022. "Nonlinear dynamical modelling of high frequency electrostatic drift waves using fluid theoretical approach in magnetized plasma," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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