A STUDY OF THE DISCRETE P-V EQUATION - MIURA-TRANSFORMATIONS AND PARTICULAR SOLUTIONS

We derive the form of the Miura transformation of the discrete P-v equ ation and show that it is indeed an auto-Backlund transformation, i.e, it relates the discrete P-v to itself. Using this auto-Backlund, we o btain the Schlesinger transformations of discrete P-v which relate the solution for one set of the parameters of the equation to that of ano ther set of neighbouring parameters. Finally, we obtain particular sol utions of the discrete P-v (i.e, solutions that exist only for some sp ecific values of the parameters). These solutions are of two types: so lutions involving the confluent hypergeometric function (on codimensio n-one submanifold of parameters) and rational solutions (on codimensio n-two submanifold of parameters).