Soliton hierarchies associated with Lie algebra sp(6)

2025/07/01 by Yanhui Bi, Bi, Yanhui, Ruan, Yuqi +4
Mathematics · Physics and Astronomy · #17B10 #34A26 (Primary) #34C14 #58A30 (Secondary) #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2507.00559

openalex publication_date 2025/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, by selecting appropriate spectral matrices within the loop algebra of symplectic Lie algebra sp(6), we construct two distinct classes of integrable soliton hierarchies. Then, by employing the Tu scheme and trace identity, we derive the Hamiltonian structures of the aforementioned two classes of integrable systems. From these two classes of integrable soliton hierarchies, we select one particular hierarchy and employ the Kronecker product to construct an integrable coupling system.

Citations

• Algebraic structures related to integrable differential equations
• Darboux transformations of integrable couplings and applications
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems

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