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Abstract <p> We solve a unique matrix spectral problem that encompasses eight distinct potentials and subsequently derive a corresponding soliton hierarchy using the zero curvature representation. Moreover, we establish a bi-Hamiltonian framework by applying the trace identity, thereby emphasizing the Liouville integrability of the derived soliton hierarchy. Two illustrative examples are provided, including generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations, to showcase the applicability and significance of the proposed methodology. Finally, we obtain some integrable reductions within the derived soliton hierarchy. </p>

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A combined Liouville integrable hierarchy associated with a sixth-order matrix spectral problem and its integrable reductions

  • 期刊论文

  • 发表日期：

    2025年12月23日

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  • Yadong Zhong,
  • Jingjing Ge,
  • Yi Zhang

摘要

Abstract

We solve a unique matrix spectral problem that encompasses eight distinct potentials and subsequently derive a corresponding soliton hierarchy using the zero curvature representation. Moreover, we establish a bi-Hamiltonian framework by applying the trace identity, thereby emphasizing the Liouville integrability of the derived soliton hierarchy. Two illustrative examples are provided, including generalized combined nonlinear Schrödinger equations and modified Korteweg–de Vries equations, to showcase the applicability and significance of the proposed methodology. Finally, we obtain some integrable reductions within the derived soliton hierarchy.