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Systems Of Partial Differential Equations And Lie Pseudogroups
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Book Synopsis Systems of Partial Differential Equations and Lie Pseudogroups by : J. F. Pommaret
Download or read book Systems of Partial Differential Equations and Lie Pseudogroups written by J. F. Pommaret and published by CRC Press. This book was released on 1978 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Systems of Linear Partial Differential Equations and Deformation of Pseudogroup Structures by : Antonio Kumpera
Download or read book Systems of Linear Partial Differential Equations and Deformation of Pseudogroup Structures written by Antonio Kumpera and published by Presses de l'Université de Montréal. This book was released on 1974 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis System of Partial Differential Equations and Lie Pseudogroups by : J. F. Pommaret
Download or read book System of Partial Differential Equations and Lie Pseudogroups written by J. F. Pommaret and published by . This book was released on 1978 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partial Differential Equations and Group Theory by : J.F. Pommaret
Download or read book Partial Differential Equations and Group Theory written by J.F. Pommaret and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lie's Structural Approach to PDE Systems by : Olle Stormark
Download or read book Lie's Structural Approach to PDE Systems written by Olle Stormark and published by Cambridge University Press. This book was released on 2000-06-15 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lie Pseudogroups and Mechanics by : J. F. Pommaret
Download or read book Lie Pseudogroups and Mechanics written by J. F. Pommaret and published by CRC Press. This book was released on 1988 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie-Theoretic Ode Numerical Analysis, Mechanics and Differential Systems by : Robert Hermann
Download or read book Lie-Theoretic Ode Numerical Analysis, Mechanics and Differential Systems written by Robert Hermann and published by Math-Sci Press. This book was released on 1994 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Approaches to Differential Equations by : Peter J. Vassiliou
Download or read book Geometric Approaches to Differential Equations written by Peter J. Vassiliou and published by Cambridge University Press. This book was released on 2000-03-13 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise and accessible introduction to the wide range of topics in geometric approaches to differential equations.
Book Synopsis Symmetries, Differential Equations and Applications by : Victor G. Kac
Download or read book Symmetries, Differential Equations and Applications written by Victor G. Kac and published by Springer. This book was released on 2018-11-04 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether’s Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.
Book Synopsis Symmetries and Overdetermined Systems of Partial Differential Equations by : Michael Eastwood
Download or read book Symmetries and Overdetermined Systems of Partial Differential Equations written by Michael Eastwood and published by Springer Science & Business Media. This book was released on 2009-04-23 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis New Mathematical Methods for Physics by : Jean-Francois Pommaret
Download or read book New Mathematical Methods for Physics written by Jean-Francois Pommaret and published by . This book was released on 2018-06 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of "group" has been introduced in mathematics for the first time by E. Galois (1830) and slowly passed from algebra to geometry with the work of S. Lie on Lie groups (1880) and Lie pseudogroups (1890) of transformations. The concept of a finite length differential sequence, now called the Janet sequence, had been described for the first time by M. Janet (1920). Then, the work of D. C. Spencer (1970) has been the first attempt to use the formal theory of systems of partial differential equations (PDE) in order to study the formal theory of Lie pseudogroups. However, the linear and nonlinear Spencer sequences for Lie pseudogroups, though never used in physics, largely supersede the "Cartan structure equations " (1905) and are quite different from the "Vessiot structure equations " (1903), introduced for the same purpose but never acknowledged by E. Cartan or successors. Meanwhile, mixing differential geometry with homological algebra, M. Kashiwara (1970) created "algebraic analysis" in order to study differential modules and double duality. By chance, unexpected arguments have been introduced by the brothers E. and F. Cosserat (1909) in order to revisit elasticity and by H. Weyl (1918) in order to revisit electromagnetism through a unique differential sequence only depending on the structure of the conformal group of space-time.The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of the extension. It has been the dream of many mathematicians at the end of the nineteenth century to generalize these results to systems of linear or algebraic PDE and the corresponding finitely generated differential extensions, in order to be able to add the word differential in front of any classical statement. The achievement of the Picard-Vessiot theory by E. Kolchin and coworkers between 1950 and 1970 is now well-known. However, the work of Vessiot on the differential Galois theory (1904), that is on the possibility to extend the classical Galois theory to systems of algebraic PDE and algebraic Lie pseudogroups, namely groups of transformations solutions for systems of algebraic PDE, has also never been acknowledged. His main idea has been to notice that the Galois theory (old and new) is a study of principal homogeneous spaces (PHS) for algebraic groups or pseudogroups described by what he called "automorphic systems" of PDE.The purpose of this book is first to revisit Gauge Theory and General Relativity in light of the latest developments just described and then to apply the differential Galois theory in order to revisit various domains of mechanics (Shell theory, Chain theory, Frenet-Serret formulas, Hamilton-Jacobi equations). All the results presented are new. (Nova)
Book Synopsis An Introduction to the Lie Theory of One-parameter Groups by : Abraham Cohen
Download or read book An Introduction to the Lie Theory of One-parameter Groups written by Abraham Cohen and published by . This book was released on 1911 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applications of Lie Groups to Differential Equations by : Peter J. Olver
Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Methods for Constructing Exact Solutions of Partial Differential Equations by : Sergey V. Meleshko
Download or read book Methods for Constructing Exact Solutions of Partial Differential Equations written by Sergey V. Meleshko and published by Springer Science & Business Media. This book was released on 2005-09-16 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.
Book Synopsis Group Theory and Numerical Analysis by : Pavel Winternitz
Download or read book Group Theory and Numerical Analysis written by Pavel Winternitz and published by American Mathematical Soc.. This book was released on with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop on Group Theory and Numerical Analysis brought together scientists working in several different but related areas. The unifying theme was the application of group theory and geometrical methods to the solution of differential and difference equations. The emphasis was on the combination of analytical and numerical methods and also the use of symbolic computation. This meeting was organized under the auspices of the Centre de Recherches Mathematiques, Universite de Montreal (Canada). This volume has the character of a monograph and should represent a useful reference book for scientists working in this highly topical field.
Book Synopsis Elie Cartan (1869-1951) by : M. A. Akivis
Download or read book Elie Cartan (1869-1951) written by M. A. Akivis and published by American Mathematical Soc.. This book was released on 2011-07-14 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.
Book Synopsis Numerical Mathematics and Advanced Applications by : Karl Kunisch
Download or read book Numerical Mathematics and Advanced Applications written by Karl Kunisch and published by Springer Science & Business Media. This book was released on 2008-09-19 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) is a series of conferences held every two years to provide a forum for discussion on recent aspects of numerical mathematics and their applications. The ?rst ENUMATH conference was held in Paris (1995), and the series continued by the one in Heidelberg (1997), Jyvaskyla (1999), Ischia (2001), Prague (2003), and Santiago de Compostela (2005). This volume contains a selection of invited plenary lectures, papers presented in minisymposia, and contributed papers of ENUMATH 2007, held in Graz, Austria, September 10–14, 2007. We are happy that so many people have shown their interest in this conference. In addition to the ten invited presentations and the public lecture, we had more than 240 talks in nine minisymposia and ?fty four sessions of contributed talks, and about 316 participants from all over the world, specially from Europe. A total of 98 contributions appear in these proceedings. Topics include theoretical aspects of new numerical techniques and algorithms, as well as to applications in engineering and science. The book will be useful for a wide range of readers, giving them an excellent overview of the most modern methods, techniques, algorithms and results in numerical mathematics, scienti?c computing and their applications. We would like to thank all the participants for the attendance and for their va- ablecontributionsanddiscussionsduringtheconference.Specialthanksgothe m- isymposium organizers, who made a large contribution to the conference, the chair persons, and all speakers.