Soliton equations related to the affine Kac-Moody algebra D^(1)_4

Abstract

We have derived the hierarchy of soliton equations associated with the untwisted affine Kac-Moody algebra D^(1)_4 by calculating the corresponding recursion operators. The Hamiltonian formulation of the equations from the hierarchy is also considered. As an example we have explicitly presented the first non-trivial member of the hierarchy, which is an one-parameter family of mKdV equations. We have also considered the spectral properties of the Lax operator and introduced a minimal set of scattering data.

27 pages. V2: 30 pages, 1 figure. Improvements in the whole text, typos corrected, references added. V3: 30 pages, 1 figure. Minor changes