Lie-algebraic structure of the Lax-integrable (2| 1+ 1) -dimensional supersymmetric matrix dynamical systems

Abstract

By using a specially constructed Backlund transformation, we obtain the Hamiltonian representation for the hierarchy of Laxtype flows on the dual space to the Lie algebra of matrix superintegral-differential operators with one anticommutative variable, coupled with suitable evolutions of eigenfunctions and adjoint eigenfunctions of the associated spectral problems. We also propose the Hamiltonian description of the corresponding set of the hierarchies of additional homogeneous symmetries (squared eigenfunction symmetries). The connection between these hierarchies and the Lax-integrable (2| 1+1)-dimensional supersymmetric matrix nonlinear dynamical systems and their triple Lax-type linearizations is analyzed.