Supersymmetric Toda lattice hierarchies

Details Supersymmetric Toda lattice hierarchies Supersymmetric Toda lattice hierarchies

2000-11-04

arxiv.org/abs/nlin/0011009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

38 pages LaTeX, to be published in Proceedings of the NATO ARW ``Integrable Hierarchies and Modern Physical Theories'' (Chicag

Scientific paper

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.

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