Nonlinear Partial Differential Equations In Geometry And Physics
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Nonlinear Partial Differential Equations In Geometry And Physics
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Author : Garth Baker
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Nonlinear Partial Differential Equations In Geometry And Physics written by Garth Baker and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" . While the relevance of partial differential equations to problems in differen tial geometry has been recognized since the early days of the latter subject, the idea that differential equations of differential-geometric origin can be useful in the formulation of physical theories is a much more recent one. Perhaps the earliest emergence of systems of nonlinear partial differential equations having deep geo metric and physical importance were the Einstein equations of general relativity (1915). Several basic aspects of the initial value problem for the Einstein equa tions, such as existence, regularity and stability of solutions remain prime research areas today. eighty years after Einstein's work. An even more recent development is the realization that structures originally the context of models in theoretical physics may turn out to have introduced in important geometric or topological applications. Perhaps its emergence can be traced back to 1954, with the introduction of a non-abelian version of Maxwell's equations as a model in elementary-particle physics, by the physicists C.N. Yang and R. Mills. The rich geometric structure ofthe Yang-Mills equations was brought to the attention of mathematicians through work of M.F. Atiyah, :"J. Hitchin, I.
Nonlinear Partial Differential Equations In Geometry And Physics
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Author : Garth Baker
language : en
Publisher: Birkhauser
Release Date : 1997-01-01
Nonlinear Partial Differential Equations In Geometry And Physics written by Garth Baker and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Differential equations, Nonlinear categories.
This volume contains survey lectures in four different areas, delivered by leading researchers at the 1995 Barrett Lectures held at the University of Tennessee: nonlinear hyperbolic systems arising in field theory and relativity (S. Klainerman); harmonic maps from Minkowski spacetime (M. Struwe); dynamics of vortices in the Ginzburg-Landau model of superconductivity (F.-H. Lin); the Seiberg-Witten equations and their application to problems in four-dimensional topology (R. Fintushel). Most of this material has not previously been available in survey form. These lectures provide an up-to-date overview and an introduction to the research literature in each of these areas, which should prove useful to researchers and graduate students in mathematical physics, partial differential equations, differential geometry and topology.
Geometry And Nonlinear Partial Differential Equations
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Author : Vladimir Oliker
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Geometry And Nonlinear Partial Differential Equations written by Vladimir Oliker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This volume contains the proceedings of an AMS Special Session on Geometry, Physics, and Nonlinear PDEs, The conference brought together specialists in Monge-Ampere equations, prescribed curvature problems, mean curvature, harmonic maps, evolution with curvature-dependent speed, isospectral manifolds, and general relativity. An excellent overview of the frontiers of research in these areas.
Applications Of Analytic And Geometric Methods To Nonlinear Differential Equations
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Author : P.A. Clarkson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Analytic And Geometric Methods To Nonlinear Differential Equations written by P.A. Clarkson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.
Nonlinear Pdes Their Geometry And Applications
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Author : Radosław A. Kycia
language : en
Publisher: Springer
Release Date : 2019-05-18
Nonlinear Pdes Their Geometry And Applications written by Radosław A. Kycia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-18 with Mathematics categories.
This volume presents lectures given at the Summer School Wisła 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Ampère equations. Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.
Geometry And Nonlinear Partial Differential Equations
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Author : Shing-Tung Yau
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Geometry And Nonlinear Partial Differential Equations written by Shing-Tung Yau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Differential equations, Nonlinear categories.
This book presents the proceedings of a conference on geometry and nonlinear partial differential equations dedicated to Professor Buqing Su in honor of his one-hundredth birthday. It offers a look at current research by Chinese mathematicians in differential geometry and geometric areas of mathematical physics. It is suitable for advanced graduate students and research mathematicians interested in geometry, topology, differential equations, and mathematical physics.
Partial Differential Equations Arising From Physics And Geometry
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Author : Mohamed Ben Ayed
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Partial Differential Equations Arising From Physics And Geometry written by Mohamed Ben Ayed and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Mathematics categories.
Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.
Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics
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Author : Victor A. Galaktionov
language : en
Publisher: CRC Press
Release Date : 2006-11-02
Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics written by Victor A. Galaktionov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-02 with Mathematics categories.
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book
Geometric Analysis And Nonlinear Partial Differential Equations
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Author : Stefan Hildebrandt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Analysis And Nonlinear Partial Differential Equations written by Stefan Hildebrandt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is not a textbook, but rather a coherent collection of papers from the field of partial differential equations. Nevertheless we believe that it may very well serve as a good introduction into some topics of this classical field of analysis which, despite of its long history, is highly modem and well prospering. Richard Courant wrote in 1950: "It has always been a temptationfor mathematicians to present the crystallized product of their thought as a deductive general theory and to relegate the individual mathematical phenomenon into the role of an example. The reader who submits to the dogmatic form will be easily indoctrinated. Enlightenment, however, must come from an understanding of motives; live mathematical development springs from specific natural problems which can be easily understood, but whose solutions are difficult and demand new methods or more general significance. " We think that many, if not all, papers of this book are written in this spirit and will give the reader access to an important branch of analysis by exhibiting interest ing problems worth to be studied. Most of the collected articles have an extensive introductory part describing the history of the presented problems as well as the state of the art and offer a well chosen guide to the literature. This way the papers became lengthier than customary these days, but the level of presentation is such that an advanced graduate student should find the various articles both readable and stimulating.
Nonlinear Theory Of Generalized Functions
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Author : Michael Oberguggenberger
language : en
Publisher: Routledge
Release Date : 2022-02-28
Nonlinear Theory Of Generalized Functions written by Michael Oberguggenberger and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-28 with Mathematics categories.
Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.