ar X iv : s ol v - in t / 9 80 90 04 v 1 3 1 A ug 1 99 8 ALGEBRO - GEOMETRIC SOLUTIONS OF THE BOUSSINESQ HIERARCHY

ar X iv : s ol v - in t / 9 81 20 26 v 1 2 1 D ec 1 99 8 THE CLASSICAL BOUSSINESQ HIERARCHY REVISITED

We develop a systematic approach to the classical Boussinesq (cBsq) hierarchy based on an elementary polynomial recursion formalism. Moreover, the gauge equivalence between the cBsq and AKNS hierarchies is studied in detail and used to provide an effortless derivation of algebro-geometric solutions and their theta function representations of the cBsq hierarchy .

ar X iv : s ol v - in t / 9 70 80 05 v 1 1 4 A ug 1 99 7 On the Integrable Hierarchies

A new Lax operator is proposed from the viewpoint of constructing the integrable hierarchies related with N = 2 super Wn algebra. It is shown that the Poisson algebra associated to the second Hamiltonian structure for the resulted hierarchy contains the N = 2 super Virasoro algebra as a proper subalgebra. The simplest cases are discussed in detail. In particular, it is proved that the supersymm...

ar X iv : s ol v - in t / 9 80 80 19 v 1 2 7 A ug 1 99 8 Hypercomplex Integrable Systems

In this paper we study hypercomplex manifolds in four dimensions. Rather than using an approach based on differential forms, we develop a dual approach using vector fields. The condition on these vector fields may then be interpreted as Lax equations, exhibiting the integrability properties of such manifolds. A number of different field equations for such hypercomplex manifolds are derived, one...

ar X iv : s ol v - in t / 9 70 80 06 v 1 1 4 A ug 1 99 7 Introduction to the Hirota bilinear method

ar X iv : s ol v - in t / 9 70 80 01 v 1 4 A ug 1 99 7 Two - dimensional soliton cellular automaton of deautonomized Toda - type

A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed. PACS: 03.20.+i; 03.40.Kf; 04.60.Nc