From trihomographic to elliptic Painlevé equations. (24th October 2016)

• Record Type: Journal Article
• Authors: Grammaticos, B; Ramani, A
• Is Part Of: Journal of physics. Volume 49:Number 45(2016)
• Publication Date: 2016-10-24
• Subjects: discrete Painlevé equations -- elliptic equations -- affine Weyl groups -- singularity analysis; 37J35 -- 39A10 -- 39A13 -- 58K20; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/45/45LT02
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We use the trihomographic representation of discrete Painlevé equations in order to derive a new, factorised form for equations associated with the affine Weyl group E 8 ( 1 ) . Introducing an ancillary dependent variable we are able to obtain factorised forms for the general additive, multiplicative and elliptic discrete E 8 ( 1 ) -related Painlevé equations. The advantage of these factorised forms is that they make the singularity analysis of the E 8 ( 1 ) straightforward in par with the situation for equations associated with lower affine Weyl groups.