Generalized Integrable Hierarchies of AKNS Type, Super Dirac Type and Super NLS-mKdV Type

Integrable hierarchies provide many important physical models. Firstly, with the help of symbolic computation software Maple, two generalized integrable hierarchies of Ablowitz-Kaup-Newell-Segur (AKNS) type are constructed from the matrix spectral problem associated with the Lie algebra sl(2). Then, two generalized integrable hierarchies of super Dirac type and super nonlinear Schrödinger-modified Korteweg-de Vries (NLS-mKdV) type are obtained to illustrate the use of the super Lie algebra B(0,1).