Clarkson, P.A. (2005) Special polynomials associated with rational solutions of the fifth Painlevé equation. Journal of Computational and Applied Mathematics, 178 (1-2). pp. 111-129. ISSN 0377-0427 .
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In this paper special polynomials associated with rational and algebraic solutions of the fifth Painlevéequation (PV) are studied. These special polynomials defined by second-order, bilinear differential-difference equations which are equivalent to Toda equations. The structure of the zeroes of these special polynomials, which involve a parameter, is investigated and it is shown that these have an intriguing, symmetric and regular structure. For large negative values of the parameter the zeroes have an approximate triangular structure. As the parameter increases the zeroes coalesce for certain values and eventually for large positive values of the parameter the zeroes also have an approximate triangular structure, though with the orientation reversed. In fact, the interaction of the zeroes is “solitonic” in nature since the same pattern reappears, with its orientation reversed.
|Uncontrolled keywords:||Painleve equations; rational solutions; Toda equations|
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics|
|Depositing User:||Peter A Clarkson|
|Date Deposited:||06 Jun 2008 10:26|
|Last Modified:||14 Jan 2010 14:11|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/3246 (The current URI for this page, for reference purposes)|
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