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Matrix mKdV Integrable Hierarchies via Two Identical Group Reductions

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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 33620-5700, USA
    Material Science Innovation and Modelling, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa)

Abstract

This paper applies a pair of identical group reductions or similarity transformations to formulate integrable models. An application to the Ablowitz–Kaup–Newell–Segur (AKNS) matrix spectral problems leads to reduced matrix modified Korteweg–de Vries (mKdV) integrable hierarchies. In particular, several illustrative examples of reduced matrix mKdV integrable models are derived from the reduced AKNS matrix spectral problems.

Suggested Citation

  • Wen-Xiu Ma, 2025. "Matrix mKdV Integrable Hierarchies via Two Identical Group Reductions," Mathematics, MDPI, vol. 13(9), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1438-:d:1644335
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    References listed on IDEAS

    as
    1. Jian Zhang & Chiping Zhang & Yunan Cui, 2017. "Bi‐Integrable and Tri‐Integrable Couplings of a Soliton Hierarchy Associated with SO(3)," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    2. Xiao-ming Zhu & Jian-bing Zhang & Yao Zhong Zhang, 2022. "The Integrability of a New Fractional Soliton Hierarchy and Its Application," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-14, May.
    3. Xiao-ming Zhu & Jian-bing Zhang, 2022. "The Integrability of a New Fractional Soliton Hierarchy and Its Application," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    4. Song, Cai-Qin & Liu, Dan-Ya & Ma, Li-Yuan, 2024. "Soliton solutions of a novel nonlocal Hirota system and a nonlocal complex modified Korteweg–de Vries equation," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
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