A class of extended Lie superalgebras and their applications. (March 2023) - Wang, Haifeng; He, Baiying
Abstract: We construct a class of extended Lie superalgebras, including a generalized Lie superalgebra B(0, 1), a generalized Lie superalgebra spl(2, 1), a generalized Lie superalgebra spo(2, 2), and a generalized Lie superalgebra osp(2, 2). Considering the applications of these Lie superalgebras, we obtain three different nonisospectral super AKNS hierarchies. It follows that many classical and new equations are deduced by discussing some reductions of these hierarchies, such as the nonlinear Schrödinger (NLS) equation, the Burgers equation, the heat equation, the Fokker–Planck equation, the KdV equation, and so on. Based on the Killing form on these extended Lie superalgebras, we obtain the super Hamiltonian structures of these three nonisospectral super AKNS hierarchies. Highlights: We construct a class of extended Lie superalgebras. Three nonisospectral super AKNS hierarchies are obtained. The super Hamiltonian structures of these super hierarchies are obtained. The idea used here are universal for other isospectral-nonisospectral problems.