The nonisospectral integrable hierarchies of three generalized Lie algebras

Baiying He; Siyu Gao; Baiying He; Siyu Gao

doi:10.3934/math.20241329

AIMS Mathematics

2024, Volume 9, Issue 10: 27361-27387. doi: 10.3934/math.20241329

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Research article

The nonisospectral integrable hierarchies of three generalized Lie algebras

Baiying He ^,,
Siyu Gao

School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

Received: 18 August 2024 Revised: 14 September 2024 Accepted: 18 September 2024 Published: 20 September 2024
MSC : 37K05, 37K40, 35Q53

We construct the generalized Lie algebras $ \mathfrak{sp}(4) $, $ \mathfrak{so}(5) $, and $ \mathfrak{so}(3, 2) $, and derive three kinds of (1+1)-dimensional nonisospectral integrable hierarchies. Moreover, we obtain their Hamiltonian structures. Finally, based on Lie algebras $ \mathfrak{sp}(4) $, $ \mathfrak{so}(5) $, and $ \mathfrak{so}(3, 2) $, by using the semi-direct sum decomposition of Lie algebras, we construct three kinds of integrable coupling systems associated with these three Lie algebras.
- Lie algebra,
- Hamiltonian structure,
- nonisospectral integrable hierarchy,
- integrable couplings
Citation: Baiying He, Siyu Gao. The nonisospectral integrable hierarchies of three generalized Lie algebras[J]. AIMS Mathematics, 2024, 9(10): 27361-27387. doi: 10.3934/math.20241329

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Abstract

We construct the generalized Lie algebras $ \mathfrak{sp}(4) $, $ \mathfrak{so}(5) $, and $ \mathfrak{so}(3, 2) $, and derive three kinds of (1+1)-dimensional nonisospectral integrable hierarchies. Moreover, we obtain their Hamiltonian structures. Finally, based on Lie algebras $ \mathfrak{sp}(4) $, $ \mathfrak{so}(5) $, and $ \mathfrak{so}(3, 2) $, by using the semi-direct sum decomposition of Lie algebras, we construct three kinds of integrable coupling systems associated with these three Lie algebras.

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