A class of extended Lie superalgebras and their applications

Haifeng Wang and Baiying He

Chaos, Solitons & Fractals, 2023, vol. 168, issue C

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.

Keywords: Lie superalgebra; Super Hamiltonian structure; Nonisospectral super integrable hierarchy (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000462

DOI: 10.1016/j.chaos.2023.113145

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