v - in t / 9 61 20 07 v 1 1 9 D ec 1 99 6 Multidimensional Quadrilateral Lattices are Integrable

ar X iv : g r - qc / 9 61 20 58 v 1 2 0 D ec 1 99 6 INTEGRABLE 1 + 1 DIMENSIONAL GRAVITY MODELS

Integrable models of dilaton gravity coupled to electromagnetic and scalar matter fields in dimensions 1+1 and 0+1 are reviewed. The 1+1 dimensional integrable models are either solved in terms of explicit quadratures or reduced to the classically integrable Li-ouville equation. The 0+1 dimensional integrable models emerge as sectors in generally non integrable 1+1 dimensional models and can be...

ar X iv : s ol v - in t / 9 61 20 02 v 1 4 D ec 1 99 6 Correlators of the phase model

We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the " darkness formation probability " are calculated in the thermodynamical limit. These results can be used to construct integrable equations for the correlation functions and to calculate their asymptotics.

ar X iv : s ol v - in t / 9 61 20 02 v 2 2 0 D ec 1 99 6 Correlators of the phase model

We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the " darkness formation probability " are calculated in the thermodynamical limit. These results can be used to construct integrable equations for the correlation functions and to calculate their asymptotics.

ar X iv : g r - qc / 9 61 20 09 v 1 3 D ec 1 99 6 Signal analysis of gravitational waves

ar X iv : q - a lg / 9 61 20 14 v 1 1 1 D ec 1 99 6 Integral soluitons of q - difference equations

Two integral solutions of q-difference equations of the hypergeometric type with |q| = 1 are constructed by using the double sine function. One is an integral of the Barnes type and the other is of the Euler type.