Supersymmetric Toda lattice hierarchies
Abstract
The origin of the bosonic and fermionic solutions, constructed in [1,2,3], to the symmetry equations corresponding to the two-dimensional bosonic and N=(2|2) supersymmetric Toda lattices is established, and algebras of the corresponding symmetries are derived. The conjecture regarding an N=(2|2) superfield formulation of the N=(2|2) supersymmetric Toda lattice hierarchy, proposed in [16], is proved. The two-dimensional N=(0|2) supersymmetric Toda lattice hierarchy is proposed and its N=(0|2) superfield formulation is discussed. Bosonic and fermionic solutions to the symmetry equation corresponding to the two-dimensional N=(0|2) supersymmetric Toda lattice equation and their algebra are constructed. An infinite class of new two-dimensional supersymmetric Toda-type hierarchies is discussed.
Keywords
Cite
@article{arxiv.nlin/0011009,
title = {Supersymmetric Toda lattice hierarchies},
author = {V. G. Kadyshevsky and A. S. Sorin},
journal= {arXiv preprint arXiv:nlin/0011009},
year = {2007}
}
Comments
38 pages LaTeX, to be published in Proceedings of the NATO ARW ``Integrable Hierarchies and Modern Physical Theories'' (Chicago, USA, July 22 - 26, 2000), Kluwer Academic Publishers