Toda lattice realization of integrable hierarchies

Abstract

We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudodifferential Lax operator, can be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda lattice hierarchy seems to be as general as the Drinfeld--Sokolov realization.

11 pages, Latex (minor changes, to appear in Lett.Math.Phys.)

References in corpus (4)

• On Two-Current Realization of KP Hierarchy
• Multi-field representations of KP hierarchies and multi-matrix models
• On the constrained KP hierarchy
• The (N,M)-th KdV hierarchy and the associated W algebra