Author

Paul Bracken

Department of Mathematics, University of Texas, Edinburg, TX, United States

4 articles in our journals

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Research ArticleOpen accessAsymptotic Analysis and Convergence of Recursively Defined SequencesPaul BrackenThe asymptotic properties and limiting behavior of several distinct real sequences are determined. These sequences are defined by means of recurrence relations. Divergent and convergent sequences are discussed. It is shown methods can be found to treat both kinds producing definite knowledge with regard to the sequence. In the case of divergence, a related convergent subsequence can often be found … …Journal of Mathematics and Statistics, Vol. 22, Issue 1 · 1 Oct 2026 · 538 accessesView PDF Cite

Research ArticleOpen accessIntegrability and Prolongation Structure of a Generalized Korteweg-de Vries EquationPaul BrackenA closed differential ideal is constructed for a generalized Korteweg-de Vries equation. The ideal can be used to establish integrability for the equation. Some prolongation structures are determined for the equation and some larger prolongation algebras for given instances of the equation are found. The significance of this is that Backlund transformations can be developed based on them. It is … …Journal of Mathematics and Statistics, Vol. 6, Issue 2 · 30 Jun 2010 · 7,411 accessesView PDF Cite

Research ArticleOpen accessSplit-Quaternionic Representation of the Moving Frame for Timelike Surfaces in 3-Dimensional Minkowski SpacetimePaul BrackenThe moving frame and associated Gauss-Codazzi equations for surfaces in Minkowski three space are introduced. A split-quaternionic representation is used to identify the Gauss-Weingarten equations with a Lax pair representation. This Lax pair representaion is calculated and given explicitly. …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 7,725 accessesView PDF Cite

Research ArticleOpen accessExterior Differential Systems for Higher Order Partial Differential EquationsPaul BrackenThe theory of exterior differential systems is applied to study integrability of a set of related partial differential equations expressed in the terms of differential forms using Cartan's method. The Camassa-Holm equation and the Degasperis-Procesi equations are special cases that are described by these exterior differential systems. Some conservation laws are obtained in the cases of the more relevant equations. … …Journal of Mathematics and Statistics, Vol. 6, Issue 1 · 31 Mar 2010 · 6,924 accessesView PDF Cite