symmetric differential equations

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Symmetry Methods For Differential Equations

Author : Peter E. Hydon
ISBN : 0521497868
Genre : Mathematics
File Size : 49. 19 MB
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An introduction to symmetry methods, informally written and aimed at applied mathematicians, physicists, and engineers.

Symmetry And Integration Methods For Differential Equations

Author : George Bluman
ISBN : 9780387216492
Genre : Mathematics
File Size : 86. 39 MB
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This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.

Applications Of Symmetry Methods To Partial Differential Equations

Author : George W. Bluman
ISBN : 9780387680286
Genre : Mathematics
File Size : 50. 79 MB
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This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.

Symmetry Analysis Of Differential Equations

Author : Daniel J. Arrigo
ISBN : 9781118721407
Genre : Mathematics
File Size : 55. 55 MB
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A SELF-CONTAINED INTRODUCTION TO THE METHODS AND TECHNIQUESOF SYMMETRY ANALYSIS USED TO SOLVE ODEs AND PDEs Symmetry Analysis of Differential Equations: AnIntroduction presents an accessible approach to the uses ofsymmetry methods in solving both ordinary differential equations(ODEs) and partial differential equations (PDEs). Providingcomprehensive coverage, the book fills a gap in the literature bydiscussing elementary symmetry concepts and invariance, includingmethods for reducing the complexity of ODEs and PDEs in an effortto solve the associated problems. Thoroughly class-tested, the author presents classical methods in asystematic, logical, and well-balanced manner. As the bookprogresses, the chapters graduate from elementary symmetries andthe invariance of algebraic equations, to ODEs and PDEs, followedby coverage of the nonclassical method and compatibility.Symmetry Analysis of Differential Equations: An Introductionalso features: Detailed, step-by-step examples to guide readers through themethods of symmetry analysis End-of-chapter exercises, varying from elementary to advanced,with select solutions to aid in the calculation of the presentedalgorithmic methods Symmetry Analysis of Differential Equations: An Introduction isan ideal textbook for upper-undergraduate and graduate-levelcourses in symmetry methods and applied mathematics. The book isalso a useful reference for professionals in science, physics, andengineering, as well as anyone wishing to learn about the use ofsymmetry methods in solving differential equations. DANIEL J. ARRIGO, PhD, is Professor in the Department ofMathematics at the University of Central Arkansas. The author ofover 30 journal articles, his research interests include theconstruction of exact solutions of PDEs; symmetry analysis ofnonlinear PDEs; and solutions to physically important equations,such as nonlinear heat equations and governing equations modelingof granular materials and nonlinear elasticity. In 2008, Dr. Arrigoreceived the Oklahoma-Arkansas Section of the MathematicalAssociation of America’s Award for Distinguished Teaching ofCollege or University Mathematics.

Symmetry Analysis Of Differential Equations With Mathematica

Author : Gerd Baumann
ISBN : 9781461221104
Genre : Mathematics
File Size : 43. 59 MB
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The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations.

Applications Of Lie Groups To Differential Equations

Author : Peter J. Olver
ISBN : 9781468402742
Genre : Mathematics
File Size : 52. 46 MB
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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.

On The Weak Symmetry Groups Of Partial Differential Equations

Author : Edvige Pucci
ISBN : CORNELL:31924058547682
Genre :
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Symmetries And Recursion Operators For Classical And Supersymmetric Differential Equations

Author : I.S. Krasil'shchik
ISBN : 9789401731966
Genre : Mathematics
File Size : 34. 65 MB
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To our wives, Masha and Marian Interest in the so-called completely integrable systems with infinite num ber of degrees of freedom was aroused immediately after publication of the famous series of papers by Gardner, Greene, Kruskal, Miura, and Zabusky [75, 77, 96, 18, 66, 19J (see also [76]) on striking properties of the Korteweg-de Vries (KdV) equation. It soon became clear that systems of such a kind possess a number of characteristic properties, such as infinite series of symmetries and/or conservation laws, inverse scattering problem formulation, L - A pair representation, existence of prolongation structures, etc. And though no satisfactory definition of complete integrability was yet invented, a need of testing a particular system for these properties appeared. Probably one of the most efficient tests of this kind was first proposed by Lenard [19]' who constructed a recursion operator for symmetries of the KdV equation. It was a strange operator, in a sense: being formally integro-differential, its action on the first classical symmetry (x-translation) was well-defined and produced the entire series of higher KdV equations; but applied to the scaling symmetry, it gave expressions containing terms of the type J u dx which had no adequate interpretation in the framework of the existing theories. It is not surprising that P. Olver wrote "The de duction of the form of the recursion operator (if it exists) requires a certain amount of inspired guesswork. . . " [80, p.

Crc Handbook Of Lie Group Analysis Of Differential Equations

Author : Nail H. Ibragimov
ISBN : 0849394198
Genre : Mathematics
File Size : 73. 69 MB
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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.

Algorithmic Lie Theory For Solving Ordinary Differential Equations

Author : Fritz Schwarz
ISBN : 1584888903
Genre : Mathematics
File Size : 40. 66 MB
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Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete problems. Taking this approach, Algorithmic Lie Theory for Solving Ordinary Differential Equations serves as a valuable introduction for solving differential equations using Lie's theory and related results. After an introductory chapter, the book provides the mathematical foundation of linear differential equations, covering Loewy's theory and Janet bases. The following chapters present results from the theory of continuous groups of a 2-D manifold and discuss the close relation between Lie's symmetry analysis and the equivalence problem. The core chapters of the book identify the symmetry classes to which quasilinear equations of order two or three belong and transform these equations to canonical form. The final chapters solve the canonical equations and produce the general solutions whenever possible as well as provide concluding remarks. The appendices contain solutions to selected exercises, useful formulae, properties of ideals of monomials, Loewy decompositions, symmetries for equations from Kamke's collection, and a brief description of the software system ALLTYPES for solving concrete algebraic problems.

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