Download Full eBooks in PDF
Systems Of Partial Differential Equations And Lie Pseudogroups Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Systems Of Partial Differential Equations And Lie Pseudogroups book. This book definitely worth reading, it is an incredibly well-written.
Author : J. F. Pommaret
Publisher : CRC Press
Page : 428 pages
File Size : 40,8 Mb
Release : 1978
Category : Mathematics
ISBN : 067700270X
Author : Antonio Kumpera,Donald Clayton Spencer,Université de Montréal. Département de mathématiques
Publisher : Presses de l'Université de Montréal
Page : 108 pages
File Size : 52,5 Mb
Release : 1974
Category : Differential equations, Linear
ISBN : UOM:39015039390003
The main goal of these notes is the description of a non-linear complex into which the integrability (or compatibility) condition is inserted as a non-linear operator in such a way that exactness implies the integrability of the almost-structure (existence of local coordinates for the structure) or, by the introduction of parameters, the existence of a (germ of) deformation of the structure. To the non-linear complex are attached some fundamental identities and a structure equation. The non-linear complex is a finite form of the initial portion of a linear complex which is a differential graded Lie algebra. The operators in the non-linear and linear complexes are of first order.
Author : J.F. Pommaret
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 47,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401725392
Ordinary differential control thPory (the classical theory) studies input/output re lations defined by systems of ordinary differential equations (ODE). The various con cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry.
Author : Olle Stormark
Publisher : Cambridge University Press
Page : 604 pages
File Size : 46,9 Mb
Release : 2000-06-15
Category : Mathematics
ISBN : 0521780888
Here is a lucid and comprehensive introduction to the differential geometric study of partial differential equations (PDE). The first book to present substantial results on local solvability of general and nonlinear PDE systems without using power series techniques, it describes a general approach to PDE systems based on ideas developed by Lie, Cartan and Vessiot. The central theme is the exploitation of singular vector field systems and their first integrals. These considerations naturally lead to local Lie groups, Lie pseudogroups and the equivalence problem, all of which are covered in detail. This book will be a valuable resource for graduate students and researchers in partial differential equations, Lie groups and related fields.
Author : Michael Eastwood,Willard Miller
Publisher : Springer Science & Business Media
Page : 565 pages
File Size : 49,7 Mb
Release : 2009-04-23
Category : Mathematics
ISBN : 9780387738314
This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
Author : Peter J. Olver
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402742
This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.
Author : J. F. Pommaret
Publisher : CRC Press
Page : 612 pages
File Size : 43,8 Mb
Release : 1988
Category : Mathematics
ISBN : 2881242138
Author : A.M. Vinogradov
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400919488
2 The authors of these issues involve not only mathematicians, but also speci alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field. A. M. VINOGRADOV 3 Acta Applicandae Mathematicae 15: 3-21, 1989. © 1989 Kluwer Academic Publishers. Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results A. M. VINOORADOV Department of Mathematics, Moscow State University, 117234, Moscow, U. S. S. R. (Received: 22 August 1988) Abstract. The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed. AMS subject classifications (1980). 35A30, 58005, 58035, 58H05. Key words. Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions. o. Introduction In this paper we present the basic notions and results from the general theory of local symmetries and conservation laws of partial differential equations. More exactly, we will focus our attention on the main conceptual points as well as on the problem of how to find all higher symmetries and conservation laws for a given system of partial differential equations. Also, some general views and perspectives will be discussed.
Author : Peter J. Vassiliou,Ian G. Lisle
Publisher : Cambridge University Press
Page : 242 pages
File Size : 54,6 Mb
Release : 2000-03-13
Category : Mathematics
ISBN : 0521775981
A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.
Author : L Dresner
Publisher : CRC Press
Page : 242 pages
File Size : 54,7 Mb
Release : 1998-01-01
Category : Science
ISBN : 1420050788
Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.
Author : Basil Nicolaenko,Darryl D. Holm,James M. Hyman
Publisher : American Mathematical Soc.
Page : 494 pages
File Size : 46,6 Mb
Release : 1986
Category : Mathematics
ISBN : 0821811258
Focusing on the increased interplay of theoretical advances in nonlinear hyperbolic systems, completely integrable systems, and evolutionary systems of nonlinear partial differential equations, this title contains papers grouped in sections: integrable systems, hyperbolic systems, variational problems, evolutionary systems, and dispersive systems.
Author : J. F. Pommaret
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 53,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0792370368
Author : A. Isidori
Publisher : Elsevier
Page : 429 pages
File Size : 45,6 Mb
Release : 2014-05-23
Category : Technology & Engineering
ISBN : 9781483298924
In the last two decades, the development of specific methodologies for the control of systems described by nonlinear mathematical models has attracted an ever increasing interest. New breakthroughs have occurred which have aided the design of nonlinear control systems. However there are still limitations which must be understood, some of which were addressed at the IFAC Symposium in Capri. The emphasis was on the methodological developments, although a number of the papers were concerned with the presentation of applications of nonlinear design philosophies to actual control problems in chemical, electrical and mechanical engineering.
Author : Nail H. Ibragimov
Publisher : CRC Press
Page : 572 pages
File Size : 54,6 Mb
Release : 1995-10-24
Category : Mathematics
ISBN : 0849394198
Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.
Author : N.H. Ibragimov,M. Torrisi,A. Valenti
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 44,9 Mb
Release : 2011-06-27
Category : Mathematics
ISBN : 9789401120500
On the occasion of the 150th anniversary of Sophus Lie, an International Work shop "Modern Group Analysis: advanced analytical and computational methods in mathematical physics" has been organized in Acireale (Catania, Sicily, October 27 31, 1992). The Workshop was aimed to enlighten the present state ofthis rapidly expanding branch of applied mathematics. Main topics of the Conference were: • classical Lie groups applied for constructing invariant solutions and conservation laws; • conditional (partial) symmetries; • Backlund transformations; • approximate symmetries; • group analysis of finite-difference equations; • problems of group classification; • software packages in group analysis. The success of the Workshop was due to the participation of many experts in Group Analysis from different countries. This book consists of selected papers presented at the Workshop. We would like to thank the Scientific Committee for the generous support of recommending invited lectures and selecting the papers for this volume, as well as the members of the Organizing Committee for their help. The Workshop was made possible by the financial support of several sponsors that are listed below. It is also a pleasure to thank our colleague Enrico Gregorio for his invaluable help of this volume.
