By analogy to the continuous Painleve-II equation, we present particular solutions of the discrete Painleve-II (d-PII) equation. These solutions are of a rational and special function (Airy) type. Our analysis is based on the bilinear formalism that allows us to obtain the tau -function for d-PII. Two different forms of bilinear d-PII are obtained and we show that they can be related by a simple gauge transformation.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics