A study of the discrete Pvequation: Miura transformations and particular solutions

✍ Scribed by K. M. Tamizhmani; A. Ramani; B. Grammaticos; Y. Ohta

• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 389 KB
• Volume: 38
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00398353

✦ Synopsis

We derive the form of the Miura transformation of the discrete Pv equation and show that it is indeed an auto-B~icklund transformation, i.e. it relates the discrete Pv to itself. Using this auto-B~icklund, we obtain the Schlesinger transformations of discrete Pv which relate the solution for one set of the parameters of the equation to that of another set of neighbouring parameters. Finally, we obtain particular solutions of the discrete Pv (i.e. solutions that exist only for some specific values of the parameters). These solutions are of two types: solutions involving the confluent hypergeometric function (on codimension-one submanifold of parameters) and rational solutions (on codimension-two submanifold of parameters).