IJPAM: Volume 100, No. 1 (2015)

CONNECTIONS OF ZERO CURVATURE
AND BÄCKLUND TRANSFORMATIONS

Paul Bracken
Department of Mathematics
University of Texas
Edinburg, TX78540, USA


Abstract. Zero curvature connections in a principal bundle are introduced. It is shown that such connections are very useful in formulating the Bäcklund problem and in constructing transformations. A general technique can be proposed for producing such transformations by defining the relevant connection coefficients appropriately. Finally, several applications of this work to various types of nonlinear partial differential equations will be presented.

Received: January 19, 2015

AMS Subject Classification: 53Z05, 57R99, 55R10, 53B50

Key Words and Phrases: connection, bundle, curvature, structure equations, Lax pair, Bäcklund

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DOI: 10.12732/ijpam.v100i1.9 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 100
Issue: 1
Pages: 95 -


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).