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Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation

Ormerod, Christopher M. (2014) Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation. Symmetry, Integrability and Geometry, Methods and Applications (SIGMA), 10 . pp. 1-19. ISSN 1815-0659.

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We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E^(1)_6 symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.

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Additional Information:© 2014 The author. The authors retain ownership of the copyright with respect to their papers published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. Received September 19, 2013, in final form December 28, 2013; Published online January 03, 2014. This research is supported by Australian Research Council Discovery Grant #DP110100077.
Funding AgencyGrant Number
Australian Research CouncilDP110100077
Subject Keywords:difference equations; integrability; reduction; isomonodromy
Classification Code:2010 Mathematics Subject Classification: 39A10; 37K15; 33C05
Record Number:CaltechAUTHORS:20140516-132702470
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:45811
Deposited By: Tony Diaz
Deposited On:16 May 2014 22:39
Last Modified:11 Sep 2015 19:33

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