A class of extended high-dimensional nonisospectral KdV hierarchies and symmetry

2022/01/10 by Haifeng Wang, Yufeng Zhang, Wang, Haifeng +2
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2201.03205

openalex publication_date 2022/01/10 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/01

Abstract

We construct a new class of N-dimensional Lie algebras and apply them to integrable systems. In this paper, we obtain a nonisospectral KdV integrable hierarchy by introducing a nonisospectral spectral problem. Then, a coupled nonisospectral KdV hierarchy is deduced by means of the corresponding higher-dimensional loop algebra. It follows that the K symmetries, τ symmetries and their Lie algebra of the coupled nonisospectral KdV hierarchy are investigated. The bi-Hamiltonian structures of the both resulting hierarchies are derived by using the trace identity. Finally, we derive a multi-component nonisospectral KdV hierarchy related to the N-dimensional loop algebra, which generalizes the coupled results to an arbitrary number of components.

Related

• The nonisospectral integrable hierarchies associated with Lie algebra \mathfraksp(6)
• Generation of higher-dimensional isospectral-nonisospectral integrable hierarchies associated with a new class of higher-dimensional column-vector loop algebras
• A family of S-mKdV hierarchy of equations and its expanding integrable models
• A new super integrable hierarchy and a generalized super-AKNS hierarchy
• Integrable couplings of a generalized D-Kaup-Newell hierarchy and their Hamiltonian structures