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Lie Backlund Transformations In Applications
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Book Synopsis Lie-Backlund Transformations in Applications by : Robert L. Anderson
Download or read book Lie-Backlund Transformations in Applications written by Robert L. Anderson and published by SIAM. This book was released on 1979-06-01 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title presents an introduction to the classical treatment of Backlund and general surface transformations; and includes detailed and accessible techniques for constructing both groups of tranformations which will be of great value to the scientist and engineer in the analysis of mathematical models of physical phenomena. Classical and recent examples of Backlund transformations as applied to geometry, nonlinear optics, turbulence models, nonlinear waves and quantum mechanics are given. The authors discuss applications of Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity.
Book Synopsis Lie-Bäcklund Transformations in Applications by : Robert L. Anderson
Download or read book Lie-Bäcklund Transformations in Applications written by Robert L. Anderson and published by . This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie-Bäcklund transformations in applications by : Robert Leonard Anderson
Download or read book Lie-Bäcklund transformations in applications written by Robert Leonard Anderson and published by . This book was released on 1979 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lie-Backlund Transformations in Applications by : Robert L. Anderson
Download or read book Lie-Backlund Transformations in Applications written by Robert L. Anderson and published by SIAM. This book was released on 1979-01-01 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title presents an introduction to the classical treatment of Backlund and general surface transformations; and includes detailed and accessible techniques for constructing both groups of tranformations which will be of great value to the scientist and engineer in the analysis of mathematical models of physical phenomena. Classical and recent examples of Backlund transformations as applied to geometry, nonlinear optics, turbulence models, nonlinear waves and quantum mechanics are given. The authors discuss applications of Lie-Backlund transformations in mechanics, quantum mechanics, gas dynamics, hydrodynamics, and relativity.
Book Synopsis Ba?cklund Transformations and Their Applications by : Rogers
Download or read book Ba?cklund Transformations and Their Applications written by Rogers and published by Academic Press. This book was released on 1982-06-18 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ba?cklund Transformations and Their Applications
Book Synopsis Bäcklund and Darboux Transformations by : A. A. Coley
Download or read book Bäcklund and Darboux Transformations written by A. A. Coley and published by American Mathematical Soc.. This book was released on 2001-01-01 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1980 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis CRC Handbook of Lie Group Analysis of Differential Equations by : Nail H. Ibragimov
Download or read book CRC Handbook of Lie Group Analysis of Differential Equations written by Nail H. Ibragimov and published by CRC Press. This book was released on 1995-10-24 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Perspectives of Nonlinear Dynamics: Volume 2 by : E. Atlee Jackson
Download or read book Perspectives of Nonlinear Dynamics: Volume 2 written by E. Atlee Jackson and published by CUP Archive. This book was released on 1989 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.
Book Synopsis Perspectives of Nonlinear Dynamics: Volume 1 by : E. Atlee Jackson
Download or read book Perspectives of Nonlinear Dynamics: Volume 1 written by E. Atlee Jackson and published by CUP Archive. This book was released on 1989 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of physical, chemical, biological, or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. This book is a comprehensive introduction to this field, suited to a broad readership, and reflecting a wide range of applications. Some of the concepts considered are: topological equivalence; embeddings; dimensions and fractals; Poincaré maps and map-dynamics; empirical computational sciences vis-á-vis mathematics; Ulam's synergetics; Turing's instability and dissipative structures; chaos; dynamic entropies; Lorenz and Rossler models; predator-prey and replicator models; FPU and KAM phenomena; solitons and nonsolitons; coupled maps and pattern dynamics; cellular automata.
Book Synopsis Transformation Groups Applied to Mathematical Physics by : Nail H. Ibragimov
Download or read book Transformation Groups Applied to Mathematical Physics written by Nail H. Ibragimov and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G.K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R.van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in - gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in pack ing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis CRC Handbook of Lie Group Analysis of Differential Equations, Volume I by : Nail H. Ibragimov
Download or read book CRC Handbook of Lie Group Analysis of Differential Equations, Volume I written by Nail H. Ibragimov and published by CRC Press. This book was released on 2023-08-25 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.
Book Synopsis Handbook of Differential Equations by : Daniel Zwillinger
Download or read book Handbook of Differential Equations written by Daniel Zwillinger and published by Academic Press. This book was released on 2014-05-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Differential Equations is a handy reference to many popular techniques for solving and approximating differential equations, including exact analytical methods, approximate analytical methods, and numerical methods. Topics covered range from transformations and constant coefficient linear equations to finite and infinite intervals, along with conformal mappings and the perturbation method. Comprised of 180 chapters, this book begins with an introduction to transformations as well as general ideas about differential equations and how they are solved, together with the techniques needed to determine if a partial differential equation is well-posed or what the "natural" boundary conditions are. Subsequent sections focus on exact and approximate analytical solution techniques for differential equations, along with numerical methods for ordinary and partial differential equations. This monograph is intended for students taking courses in differential equations at either the undergraduate or graduate level, and should also be useful for practicing engineers or scientists who solve differential equations on an occasional basis.
Book Synopsis Introduction to Symmetry Analysis by : Brian J. Cantwell
Download or read book Introduction to Symmetry Analysis written by Brian J. Cantwell and published by Cambridge University Press. This book was released on 2002-09-23 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.
Book Synopsis Lie and non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models by : Roman M. Cherniha
Download or read book Lie and non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models written by Roman M. Cherniha and published by MDPI. This book was released on 2018-07-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry
Book Synopsis Bäcklund and Darboux Transformations by : C. Rogers
Download or read book Bäcklund and Darboux Transformations written by C. Rogers and published by Cambridge University Press. This book was released on 2002-06-24 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the deep and fascinating connections that exist between a ubiquitous class of physically important waves known as solitons and the theory of transformations of a privileged class of surfaces as they were studied by eminent geometers of the nineteenth century. Thus, nonlinear equations governing soliton propagation and also mathematical descriptions of their remarkable interaction properties are shown to arise naturally out of the classical differential geometry of surfaces and what are termed Bäcklund-Darboux transformations.This text, the first of its kind, is written in a straightforward manner and is punctuated by exercises to test the understanding of the reader. It is suitable for use in higher undergraduate or graduate level courses directed at applied mathematicians or mathematical physics.
Book Synopsis The Philosophy and Physics of Noether's Theorems by : James Read
Download or read book The Philosophy and Physics of Noether's Theorems written by James Read and published by Cambridge University Press. This book was released on 2022-08-31 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1918, Emmy Noether, in her paper Invariante Variationsprobleme, proved two theorems (and their converses) on variational problems that went on to revolutionise theoretical physics. 100 years later, the mathematics of Noether's theorems continues to be generalised, and the physical applications of her results continue to diversify. This centenary volume brings together world-leading historians, philosophers, physicists, and mathematicians in order to clarify the historical context of this work, its foundational and philosophical consequences, and its myriad physical applications. Suitable for advanced undergraduate and graduate students and professional researchers, this is a go-to resource for those wishing to understand Noether's work on variational problems and the profound applications which it finds in contemporary physics.
