Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System

Abstract

Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation and $r$-matrix are also given in this paper.