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Supersymmetric Kadomtsev-Petviashvili hierarchy: “ghost” symmetry structure, reductions, and Darboux-Bäcklund solutions. (English) Zbl 0952.37035
The authors study the supersymmetric Manin-Radul-Kadomtsev-Petviashvili (MR-SKP) hierarchy of integrable supersoliton nonlinear equations within the super-pseudo-differential operator formulation. An infinite set of (anti)commuting “ghost” symmetries with the same algebra as MR-SKP is constructed and used to get systematic reduction of the original MR-SKP model to a broad class of constrained supersymmetric KP hierarchies denoted as \(\text{SKP}_{r/2,m/2}\). In the case of \(\text{SKP}_{1/2,1/2}\) it is shown that the orbit of Darboux-Bäcklund transformations lies on a supersymmetric Toda lattice being a square root of the standard one-dimensional Toda lattice. Explicit Wronskian ratio solutions for the super-tau function are determined.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
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