Supersymmetric Kadomtsev-Petviashvili hierarchy: ''Ghost'' symmetry structure, reductions, and Darboux-Backlund solutions

This paper studies Manin–Radul supersymmetric Kadomtsev–Petviashvili hierarchy (MR-SKP) in three related aspects: (i) We find an infinite set of additional (“ghost”) symmetry flows spanning the same (anti)commutation algebra as the ordinary MR-SKP flows. (ii) The latter are used to construct consistent reductions SKPr/2,m/2 of the initial unconstrained MR-SKP hierarchy which involves a nontrivial modification for the fermionic flows. (iii) For the simplest constrained MR-SKP hierarchy SKP12,12 we show that the orbit of Darboux–Backlund transformations lies on a supersymmetric Toda lattice being a square root of the standard one-dimensional Toda lattice, and also we find explicit Wronskian-ratio solutions for the super-tau function.