Affiliation:
1. School of Mathematics and Statistics, The University of Sydney, New South Wales 2006 Australia
Abstract
In this paper, we present a new method of deducing infinite sequences of exact solutions of
q
-discrete Painlevé equations by using their associated linear problems. The specific equation we consider in this paper is a
q
-discrete version of the second Painlevé equation (
q
-P
II
) with affine Weyl group symmetry of type (
A
2
+
A
1
)
(1)
. We show, for the first time, how to use the
q
-discrete linear problem associated with
q
-P
II
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
-P
II
here, is also applicable to other discrete Painlevé equations.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
5 articles.
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