ar X iv : s ol v - in t / 9 71 20 09 v 1 1 8 D ec 1 99 7 Canonical Gauge Equivalences of the sAKNS and sTB

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 71 20 13 v 1 1 9 D ec 1 99 7 A RIEMANN - HILBERT PROBLEM FOR AN ENERGY DEPENDENT SCHRÖDINGER OPERATOR

We consider an inverse scattering problem for Schrödinger operators with energy dependent potentials. The inverse problem is formulated as a RiemannHilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct symmetry classes. As an application we prove global existence theorems for the two distinct systems of partial differential equations ut + (u/2 + w)x = 0, wt ± uxxx +...

ar X iv : d g - ga / 9 71 20 20 v 1 3 0 D ec 1 99 7 Weinstein Conjecture and GW Invariants

ar X iv : g r - qc / 9 71 20 17 v 1 3 D ec 1 99 7 UAHEP 9714 Microfield Dynamics of Black Holes

The microcanonical treatment of black holes as opposed to the canonical formulation is reviewed and some major differences are displayed. In particular the decay rates are compared in the two different pictures.

ar X iv : g r - qc / 9 71 20 17 v 2 3 D ec 1 99 7 UAHEP 9714 Microfield Dynamics of Black Holes

The microcanonical treatment of black holes as opposed to the canonical formulation is reviewed and some major differences are displayed. In particular the decay rates are compared in the two different pictures.