The modified Lax and two-dimensional Toda lattice equations associated with simple Lie algebras

Abstract

We associate to each complex simple Lie algebra g a hierarchy of evolution equations; in the simplest case g = sl(2) they are the modified KdV equations. These new equations are related to the two-dimensional Toda lattice equations associated with g in the same way that the modified KdV equations are related to the sinh-Gordon equation. © 1981, Cambridge University Press. All rights reserved.