Open Access
VOL. 16 | 2015 An Application of Prolongation Algebras to Determine Bäcklund Transformations for Nonlinear Equations
Paul Bracken

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

Geom. Integrability & Quantization, 2015: 167-177 (2015) DOI: 10.7546/giq-16-2015-167-177


Prolongation algebras which are determined by applying a version of the Wahlquist-Estabrook method to three different nonlinear partial differential equations can be employed to obtain not only Lax pairs but Bäcklund transformations as well. By solving Maurer-Cartan equations for the related group specified by the prolongation algebra, a set of differential forms is obtained which can lead directly to these kinds of results. Although specific equations are studied, the approach should be applicable to large classes of partial differential equations.


Published: 1 January 2015
First available in Project Euclid: 13 July 2015

zbMATH: 1349.35329
MathSciNet: MR3363842

Digital Object Identifier: 10.7546/giq-16-2015-167-177

Rights: Copyright © 2015 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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