The nonisospectral integrable hierarchies of three generalized Lie algebras

Abstract

<p>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.</p>