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On a Schwarzian PDE associated with the KdV Hierarchy

Nijhoff, Frank W., Hone, Andrew N.W., Joshi, Nalini (2000) On a Schwarzian PDE associated with the KdV Hierarchy. Physics Letters A, 267 (2-3). pp. 147-156. ISSN 0375-9601. (doi:10.1016/S0375-9601(00)00063-3)


We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under M\"obius transformations, that is related to the Korteweg-de Vries hierarchy. In fact, this PDE can be considered as the generating equation for the entire hierarchy of Schwarzian KdV equations. We present its Lax pair, establish its connection with the SKdV hierarchy, its Miura relations to similar generating PDEs for the modified and regular KdV hierarchies and its Lagrangian structure. Finally we demonstrate that its similarity reductions lead to the {\it full} Painlev\'e VI equation, i.e. with four arbitary parameters.

Item Type: Article
DOI/Identification number: 10.1016/S0375-9601(00)00063-3
Subjects: Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew N W Hone
Date Deposited: 21 Jun 2014 23:12 UTC
Last Modified: 29 May 2019 12:42 UTC
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