Berezinian Construction of Super-Solitons in Supersymmetric Constrained KP Hierarchies

TL;DR

This paper develops a method to construct super-soliton solutions in supersymmetric KP hierarchies using Berezinian techniques, extending the integrability framework to supersymmetric models.

Contribution

It introduces a Berezinian-based approach to explicitly derive super-tau-functions for supersymmetric constrained KP hierarchies, preserving fermionic flows.

Findings

Explicit super-soliton solutions derived

Darboux-Backlund transformations preserve fermionic flows

Compatibility of reductions with supersymmetric flows established

Abstract

We consider a broad class of consistently reduced Manin-Radul supersymmetric KP hierarchies (MR-SKP) which are supersymmetric analogs of the ordinary bosonic constrained KP models. Compatibility of these reductions with the MR fermionic isospectral flows is achieved via appropriate modification of the latter preserving their (anti-)commutation algebra. Unlike the general unconstrained MR-SKP case, Darboux-Backlund transformations do preserve the fermionic isospectral flows of the reduced MR-SKP hierarchies. This allows for a systematic derivation of explicit Berezinian solutions for the super-tau-functions (super-solitons) for these models.