Supersymmetric KP Hierarchy: ``Ghost'' Symmetry Structure, Reductions and Darboux-Backlund Solutions

Abstract

This paper studies Manin-Radul supersymmetric KP 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 of the initial unconstrained MR-SKP hierarchy which involves a nontrivial modification for the fermionic flows; (iii) For the simplest constrained MR-SKP hierarchy 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.

Minor corrections in few equations. LaTeX, 12 pgs

References in corpus (3)

• Method of Squared Eigenfunction Potentials in Integrable Hierarchies of KP Type
• A New ``Dual'' Symmetry Structure of the KP Hierarchy
• The sAKNS Hierarchy

Cited by in corpus (13)

• Binary nonlinearization of the super AKNS system
• Darboux Transformation for Supersymmetric KP Hierarchies
• Binary Nonlinearization of the Super Akns System Under an Implicit Symmetry Constraint
• Supersymmetric BKP systems and their symmetries
• Odd Hamiltonian Structure for Supersymmetric Sawada - Kotera Equation
• N=2 local and N=4 nonlocal reductions of supersymmetric KP hierarchy in N=2 superspace
• Riemann-Liouville integrals of fractional order and extended KP hierarchy
• Symmetries of Supersymmetric Integrable Hierarchies of KP Type
• The Integrability of New Two-Component KdV Equation
• Real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy in real N=1 and twisted N=2 superspaces
• Supersymmetric KP hierarchy in N=1 superspace and its N=2 reductions
• The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
• Virasoro symmetries of Multi-Component Gelfand-Dickey systems