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<p>In this paper, we consider non-isospectral problems of two distinct dimensions on the loop algebra of the symplectic Lie algebra <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathfrak {sp}(6)\)</EquationSource> </InlineEquation>, and construct two integrable systems. Furthermore, we derive their Hamiltonian structures using the Tu scheme. Additionally, we construct an integrable hierarchy on the generalized Lie algebra <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathfrak {Gsp}(6)\)</EquationSource> </InlineEquation> and establish its Hamiltonian structure as well.</p>

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The Non-isospectral Integrable Hierarchies Associated with Lie Algebra \(\mathfrak {sp}(6)\)

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月20日

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  • Yanhui Bi,
  • Bo Yuan,
  • Yuqi Ruan,
  • Tao Zhang

摘要

In this paper, we consider non-isospectral problems of two distinct dimensions on the loop algebra of the symplectic Lie algebra \(\mathfrak {sp}(6)\) , and construct two integrable systems. Furthermore, we derive their Hamiltonian structures using the Tu scheme. Additionally, we construct an integrable hierarchy on the generalized Lie algebra \(\mathfrak {Gsp}(6)\) and establish its Hamiltonian structure as well.