In this paper, we present a new method of deducing infinite sequences of exact solutions of q-discrete Painleve equations by using their associated linear problems. The specific equation we consider in this paper is a q-discrete version of the second Painleve equation (q-PII) with affine Weyl group symmetry of type (A2 + A1)(1). We show, for the first time, how to use the q-discrete linear problem associated with q-PII to find an infinite sequence of exact rational solutions and also show how to find their representation as determinants by using the linear problem. The method, while demonstrated for q-PII here, is also applicable to other discrete Painlevé equations.
|Number of pages||26|
|Journal||PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES|
|Publication status||Published - 20 Jul 2011|
- Painlevé equations
- discrete equations