Research ArticleOpen accessEvery word in the titleIntegrability 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 PDFCite
Research ArticleOpen accessIn the keywordsExterior 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 PDFCite
Review ArticleOpen accessIn the abstractUsable AI: Critical Review of Its Current Issues and TrendsMajed Alshamari, Thanaa AlsalemUsable Artificial Intelligence (AI) application refers to an AI solution that is characterized by the easiness of use and learning through an optimum interface established by a proficient Human-Computer Interface (HCI) design. This article reviews the related literature to find out the importance of HCI to make AI valuable and usable. The article also investigates the possible solutions and guidelines … …Journal of Computer Science, Vol. 19, Issue 3 · 13 Feb 2023 · 8,928 accessesView PDFCite
Research ArticleOpen accessIn the abstractA New Perturbative Approach in Nonlinear Singularity AnalysisTat-Leung YeeProblem statement: The study is devoted to the “mirror” method which enables one to study the integrability of nonlinear differential equations. Approach: A perturbative extension of the mirror method is introduced. Results: The mirror system and its first perturbation are then utilized to gain insights into certain nonlinear equations possessing negative Fuchs indices, which were poorly understood in the literatures. … …Journal of Mathematics and Statistics, Vol. 7, Issue 3 · 29 Jul 2011 · 7,331 accessesView PDFCite
Research ArticleOpen accessIn the abstractSatellite's Motion under the Effect of Magnetic TorqueRashmi Bhardwaj, Parsan KaurNon-integrability of planar oscillation of a satellite in an elliptic orbit under the influence of magnetic torque has been studied. The amplitude of the oscillation remains constant upto the second order of approximation. The analysis regarding the stability of the stationary planar oscillation of a satellite near the resonance frequency shows that discontinuity occurs in the amplitude of the oscillation … …American Journal of Applied Sciences, Vol. 3, Issue 6 · 30 Jun 2006 · 6,818 accessesView PDFCite