数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (6): 2498-2508.doi: 10.1007/s10473-024-0624-y

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NOVEL INTEGRABLE HAMILTONIAN HIERARCHIES WITH SIX POTENTIALS

Wenxiu MA1,2,3,4,5   

  1. 1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;
    2. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
    3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA;
    4. Material Science Innovation and Modelling, Department of Mathematical Sciences;
    5. North-West University, Mafikeng Campus, Mmabatho 2735, South Africa
  • 收稿日期:2024-04-18 发布日期:2024-12-06
  • 作者简介:Wenxiu MA, E-mail: mawx@cas.usf.edu
  • 基金资助:
    NSFC (12271488, 11975145, 11972291), the Ministry of Science and Technology of China (G2021016032L, G2023016011L) and the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17 KJB 110020).

NOVEL INTEGRABLE HAMILTONIAN HIERARCHIES WITH SIX POTENTIALS

Wenxiu MA1,2,3,4,5   

  1. 1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;
    2. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
    3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA;
    4. Material Science Innovation and Modelling, Department of Mathematical Sciences;
    5. North-West University, Mafikeng Campus, Mmabatho 2735, South Africa
  • Received:2024-04-18 Published:2024-12-06
  • About author:Wenxiu MA, E-mail: mawx@cas.usf.edu
  • Supported by:
    NSFC (12271488, 11975145, 11972291), the Ministry of Science and Technology of China (G2021016032L, G2023016011L) and the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17 KJB 110020).

摘要: This paper aims to construct six-component integrable hierarchies from a kind of matrix spectral problems within the zero curvature formulation. Their Hamiltonian formulations are furnished by the trace identity, which guarantee the commuting property of infinitely many symmetries and conserved Hamiltonian functionals. Illustrative examples of the resulting integrable equations of second and third orders are explicitly computed.

关键词: matrix spectral problem, zero curvature equation, integrable hierarchy, NLS equations, mKdV equations

Abstract: This paper aims to construct six-component integrable hierarchies from a kind of matrix spectral problems within the zero curvature formulation. Their Hamiltonian formulations are furnished by the trace identity, which guarantee the commuting property of infinitely many symmetries and conserved Hamiltonian functionals. Illustrative examples of the resulting integrable equations of second and third orders are explicitly computed.

Key words: matrix spectral problem, zero curvature equation, integrable hierarchy, NLS equations, mKdV equations

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  • 37K15