Clarkson, P.A. (2003) Remarks on the Yablonskii–Vorob'ev polynomials. Physics Letters A, 319 (1-2). pp. 137-144. ISSN 0375-9601.
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It is well known that rational solutions of the second Painlevé equation (PII) are expressed in terms of logarithmic derivatives of the Yablonskii–Vorob'ev polynomials Qn(z) which are defined through a second order, bilinear differential-difference equation which is equivalent to the Toda equation. In this Letter, using the Hamiltonian theory for PII, it is shown that Qn(z) also satisfies a fourth order, bilinear ordinary differential equation and a fifth order, quad-linear difference equation. Further, rational solutions of some ordinary differential equations which are solvable in terms of solutions of PII are also expressed in terms of the Yablonskii–Vorob'ev polynomials.
|Uncontrolled keywords:||painleve equations; Yablonskii-Vorob'ev polynomials|
|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 10:40|
|Last Modified:||14 Jan 2010 14:11|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/3247 (The current URI for this page, for reference purposes)|
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