On the Virasoro Structure of Symmetry Algebras of Nonlinear Partial Differential Equations

We discuss Lie algebras of the Lie symmetry groups of two generically non-integrable equations in one temporal and two space dimensions arising in different contexts. The first is a generalization of the KP equation and contains 9 arbitrary functions of one and two arguments. The second one is a system of PDEs that depend on some physical parameters. We require that these PDEs are invariant under a Kac-Moody-Virasoro algebra. This leads to several limitations on the coefficients (either functions or parameters) under which equations are prime candidates for being integrable.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

On integrability of variable coefficient nonlinear Schrodinger equations

We apply Painlev\'e test to the most general variable coefficient nonlinear Schrodinger (VCNLS) equations as an attempt to identify integrable classes and compare our results versus those obtained by the use of other tools like group-theoretical approach and the Lax pairs technique of the soliton theory. We present explicit transformation formulae that can be used to generate new analytic solutions of VCNLS equations from those of the integrable NLS equation.Comment: 20 page

Generalized Kadomtsev-Petviashvili equation with an infinite dimensional symmetry algebra

A generalized Kadomtsev-Petviashvili equation, describing water waves in oceans of varying depth, density and vorticity is discussed. A priori, it involves 9 arbitrary functions of one, or two variables. The conditions are determined under which the equation allows an infinite dimensional symmetry algebra. This algebra can involve up to three arbitrary functions of time. It depends on precisely three such functions if and only if it is completely integrable.Comment: AMSLaTeX, 16 pages, no figures, corrected some typos and added two new section

A Survey on Communication Networks for Electric System Automation

Published in Computer Networks 50 (2006) 877–897, an Elsevier journal. The definitive version of this publication is available from Science Direct. Digital Object Identifier:10.1016/j.comnet.2006.01.005In today’s competitive electric utility marketplace, reliable and real-time information become the key factor for reliable delivery of power to the end-users, profitability of the electric utility and customer satisfaction. The operational and commercial demands of electric utilities require a high-performance data communication network that supports both existing functionalities and future operational requirements. In this respect, since such a communication network constitutes the core of the electric system automation applications, the design of a cost-effective and reliable network architecture is crucial. In this paper, the opportunities and challenges of a hybrid network architecture are discussed for electric system automation. More specifically, Internet based Virtual Private Networks, power line communications, satellite communications and wireless communications (wireless sensor networks, WiMAX and wireless mesh networks) are described in detail. The motivation of this paper is to provide a better understanding of the hybrid network architecture that can provide heterogeneous electric system automation application requirements. In this regard, our aim is to present a structured framework for electric utilities who plan to utilize new communication technologies for automation and hence, to make the decision making process more effective and direct.This work was supported by NEETRAC under Project #04-157