\(N = 2\) supersymmetric unconstrained matrix GNLS hierarchies are consistent (Q1024845)

The authors develop a pseudo-differential approach to the \(N=2\) supersymmetric unconstrained matrix \((k|n,m)\)-generalized nonlinear Schrödinger hierarchies in \(N=2\) superspace and rigorously construct their Lax-pair representation. This is proved to agree with the Lax-pair representation derived in the super-algebraic approach of the homogeneously-graded loop superalgebra \(sl(2k+n|2k+m)\otimes C[\lambda,\lambda^{-1}]\).