On weakly non-local, nilpotent, and super-recursion operators for N=1 super-equations
Abstract
We consider nonlinear, scaling-invariant N=1 boson + fermion supersymmetric systems whose right-hand sides are homogeneous differential polynomials and satisfy some natural assumptions. We select the super-systems that admit infinitely many higher symmetries generated by recursion operators; we further restrict ourselves to the case when the dilaton dimensions of the bosonic and fermionic super-fields coincide and the weight of the time is half the weight of the spatial variable. We discover five systems that satisfy these assumptions; one system is transformed to the purely bosonic Burgers equation. We construct local, nilpotent, triangular, weakly non-local, and super-recursion operators for their symmetry algebras.
Cite
@article{arxiv.nlin/0511056,
title = {On weakly non-local, nilpotent, and super-recursion operators for N=1 super-equations},
author = {A. V. Kiselev and T. Wolf},
journal= {arXiv preprint arXiv:nlin/0511056},
year = {2007}
}
Comments
6 pages, no figures. Proc. Int. Workshop `Supersymmetries and Quantum Symmetries-05,' JINR, Dubna, 27-31 July 2005. MSC 2000: 35Q53, 37K05, 37K10, 81T40