Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497182
Title: Painlevé equations and applications
Author: Southall, Neil J.
ISNI:       0000 0004 2673 8767
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2007
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Abstract:
The theme running throughout this thesis is the Painlevé equations, in their differential, discrete and ultra-discrete versions. The differential Painlevé equations have the Painlevé property. If all solutions of a differential equation are meromorphic functions then it necessarily has the Painlevé property. Any ODE with the Painlevé property is necessarily a reduction of an integrable PDE. Nevanlinna theory studies the value distribution and characterizes the growth of meromorphic functions, by using certain averaged properties on a disc of variable radius. We shall be interested in its well-known use as a tool for detecting integrability in difference equations—a difference equation may be integrable if it has sufficiently many finite-order solutions in the sense of Nevanlinna theory. This does not provide a sufficient test for integrability; additionally it must satisfy the well-known singularity confinement test.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.497182  DOI: Not available
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