Geometric Methods to Investigate Prolongation Structures for Differential Systems with Applications to Integrable Systems

Geometric Methods to Investigate Prolongation Structures for Differential Systems with Applications to Integrable Systems

A type of prolongation structure for several general systems is discussed. They are based on a set of one forms for which the underlying structure group of the integrability condition corresponds to the Lie algebra of SL(2,ℝ), O(3), and SU(3). Each will be considered in turn and the latter two syste...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences Vol. 2013; no. 2013; pp. 152 - 159
Main Author: Bracken, Paul
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Limiteds 2013
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects:
Differential equations
Integral equations
Mathematical research
United States
Online Access:Get full text
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Summary:A type of prolongation structure for several general systems is discussed. They are based on a set of one forms for which the underlying structure group of the integrability condition corresponds to the Lie algebra of SL(2,ℝ), O(3), and SU(3). Each will be considered in turn and the latter two systems represent larger 3×3 cases. This geometric approach is applied to all of the three of these systems to obtain prolongation structures explicitly. In both 3×3 cases, the prolongation structure is reduced to the situation of three smaller 2×2 problems.
ISSN:0161-1712
1687-0425
DOI:10.1155/2013/504645