Nonlinear integrable couplings of a generalized super Ablowitz-Kaup-Newell-Segur hierarchy and its super bi-Hamiltonian structures

Abstract

In this paper, a new generalized 5×5 matrix spectral problem of Ablowitz-Kaup-Newell-Segur type associated with the enlarged matrix Lie superalgebra is proposed, and its corresponding super soliton hierarchy is established. The super variational identities are used to furnish super Hamiltonian structures for the resulting super soliton hierarchy.