Solitons In Mathematics And Physics

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Solitons in Mathematics and Physics

Author : Alan C. Newell
Publisher : SIAM
ISBN 13 : 9781611970227
Total Pages : 260 pages
Book Rating : 4.9/5 (72 download)

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Book Synopsis Solitons in Mathematics and Physics by : Alan C. Newell

Download or read book Solitons in Mathematics and Physics written by Alan C. Newell and published by SIAM. This book was released on 1985-01-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The soliton is a dramatic concept in nonlinear science. What makes this book unique in the treatment of this subject is its focus on the properties that make the soliton physically ubiquitous and the soliton equation mathematically miraculous. Here, on the classical level, is the entity field theorists have been postulating for years: a local traveling wave pulse; a lump-like coherent structure; the solution of a field equation with remarkable stability and particle-like properties. It is a fundamental mode of propagation in gravity- driven surface and internal waves; in atmospheric waves; in ion acoustic and Langmuir waves in plasmas; in some laser waves in nonlinear media; and in many biologic contexts, such as alpha-helix proteins.

Solitons

Author : P. G. Drazin
Publisher : Cambridge University Press
ISBN 13 : 9780521336550
Total Pages : 244 pages
Book Rating : 4.3/5 (365 download)

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Book Synopsis Solitons by : P. G. Drazin

Download or read book Solitons written by P. G. Drazin and published by Cambridge University Press. This book was released on 1989-02-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to the theory of solitons in the physical sciences.

Topological Solitons

Author : Nicholas Manton
Publisher : Cambridge University Press
ISBN 13 : 1139454692
Total Pages : 507 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Topological Solitons by : Nicholas Manton

Download or read book Topological Solitons written by Nicholas Manton and published by Cambridge University Press. This book was released on 2004-06-10 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories.

Gravitational Solitons

Author : V. Belinski
Publisher : Cambridge University Press
ISBN 13 : 9781139428965
Total Pages : 280 pages
Book Rating : 4.4/5 (289 download)

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Book Synopsis Gravitational Solitons by : V. Belinski

Download or read book Gravitational Solitons written by V. Belinski and published by Cambridge University Press. This book was released on 2001-07-19 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 book gives a self-contained exposition of the theory of gravitational solitons and provides a comprehensive review of exact soliton solutions to Einstein's equations. The text begins with a detailed discussion of the extension of the Inverse Scattering Method to the theory of gravitation, starting with pure gravity and then extending it to the coupling of gravity with the electromagnetic field. There follows a systematic review of the gravitational soliton solutions based on their symmetries. These solutions include some of the most interesting in gravitational physics such as those describing inhomogeneous cosmological models, cylindrical waves, the collision of exact gravity waves, and the Schwarzschild and Kerr black holes. A valuable reference for researchers and graduate students in the fields of general relativity, string theory and cosmology, this book will also be of interest to mathematical physicists in general.

Solitons

Author : R. MacKenzie
Publisher : Springer Science & Business Media
ISBN 13 : 1461212545
Total Pages : 308 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Solitons by : R. MacKenzie

Download or read book Solitons written by R. MacKenzie and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solitons were discovered by John Scott Russel in 1834, and have interested scientists and mathematicians ever since. They have been the subject of a large body of research in a wide variety of fields of physics and mathematics, not to mention engineering and other branches of science such as biology. This volume comprises the written versions of the talks presented at a workshop held at Queen's University in 1997, an interdisciplinary meeting wherein top researchers from many fields could meet, interact, and exchange ideas. Topics covered include mathematical and numerical aspects of solitons, as well as applications of solitons to nuclear and particle physics, cosmology, and condensed-matter physics. The book should be of interest to researchers in any field in which solitons are encountered.

Soliton Theory and Its Applications

Author : Chaohao Gu
Publisher : Springer Science & Business Media
ISBN 13 : 3662031027
Total Pages : 414 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Soliton Theory and Its Applications by : Chaohao Gu

Download or read book Soliton Theory and Its Applications written by Chaohao Gu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. This book presents a broad view of soliton theory. It gives an expository survey of the most basic ideas and methods, such as physical background, inverse scattering, Backlünd transformations, finite-dimensional completely integrable systems, symmetry, Kac-moody algebra, solitons and differential geometry, numerical analysis for nonlinear waves, and gravitational solitons. Besides the essential points of the theory, several applications are sketched and some recent developments, partly by the authors and their collaborators, are presented.

Glimpses of Soliton Theory

Author : Alex Kasman
Publisher : American Mathematical Soc.
ISBN 13 : 0821852450
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Glimpses of Soliton Theory by : Alex Kasman

Download or read book Glimpses of Soliton Theory written by Alex Kasman and published by American Mathematical Soc.. This book was released on 2010 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --

Solitons, Instantons, and Twistors

Author : Maciej Dunajski
Publisher : Oxford University Press
ISBN 13 : 0198570627
Total Pages : 374 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Solitons, Instantons, and Twistors by : Maciej Dunajski

Download or read book Solitons, Instantons, and Twistors written by Maciej Dunajski and published by Oxford University Press. This book was released on 2010 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text aimed at third year undergraduates and graduates in mathematics and physics, presenting elementary twistor theory as a universal technique for solving differential equations in applied mathematics and theoretical physics.

Solitons in Field Theory and Nonlinear Analysis

Author : Yisong Yang
Publisher : Springer Science & Business Media
ISBN 13 : 1475765487
Total Pages : 571 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Solitons in Field Theory and Nonlinear Analysis by : Yisong Yang

Download or read book Solitons in Field Theory and Nonlinear Analysis written by Yisong Yang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.

Physics of Solitons

Author : Thierry Dauxois
Publisher : Cambridge University Press
ISBN 13 : 0521854210
Total Pages : 435 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Physics of Solitons by : Thierry Dauxois

Download or read book Physics of Solitons written by Thierry Dauxois and published by Cambridge University Press. This book was released on 2006-03-09 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook gives an instructive view of solitons and their applications for advanced students of physics.

Basic Methods Of Soliton Theory

Author : Ivan V Cherednik
Publisher : World Scientific
ISBN 13 : 9814499005
Total Pages : 264 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Basic Methods Of Soliton Theory by : Ivan V Cherednik

Download or read book Basic Methods Of Soliton Theory written by Ivan V Cherednik and published by World Scientific. This book was released on 1996-08-22 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.

Solitons

Author : Boling Guo
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110549638
Total Pages : 376 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Solitons by : Boling Guo

Download or read book Solitons written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-03-19 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics. Contents Introduction Inverse scattering transform Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations Interaction of solitons and its asymptotic properties Hirota method Bäcklund transformations and the infinitely many conservation laws Multi-dimensional solitons and their stability Numerical computation methods for some nonlinear evolution equations The geometric theory of solitons Global existence and blow up for the nonlinear evolution equations The soliton movements of elementary particles in nonlinear quantum field The theory of soliton movement of superconductive features The soliton movements in condensed state systemsontents

Mathematical Theory of Dispersion-Managed Optical Solitons

Author : Anjan Biswas
Publisher : Springer Science & Business Media
ISBN 13 : 3642102204
Total Pages : 170 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Mathematical Theory of Dispersion-Managed Optical Solitons by : Anjan Biswas

Download or read book Mathematical Theory of Dispersion-Managed Optical Solitons written by Anjan Biswas and published by Springer Science & Business Media. This book was released on 2010-07-07 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematical Theory of Dispersion-Managed Optical Solitons" discusses recent advances covering optical solitons, soliton perturbation, optical cross-talk, Gabitov-Turitsyn Equations, quasi-linear pulses, and higher order Gabitov-Turitsyn Equations. Focusing on a mathematical perspective, the book bridges the gap between concepts in engineering and mathematics, and gives an outlook to many new topics for further research. The book is intended for researchers and graduate students in applied mathematics, physics and engineering and also it will be of interest to those who are conducting research in nonlinear fiber optics. Dr. Anjan Biswas is an Associate Professor at the Department of Applied Mathematics & Theoretical Physics, Delaware State University, Dover, DE, USA; Dr. Daniela Milovic is an Associate Professor at the Department of Telecommunications, Faculty of Electronic Engineering, University of Nis, Serbia; Dr. Matthew Edwards is the Dean of the School of Arts and Sciences at Alabama A & M University in Huntsville, AL, USA.

The Versatile Soliton

Author : Alexandre T. Filippov
Publisher : Springer Science & Business Media
ISBN 13 : 0817649743
Total Pages : 261 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis The Versatile Soliton by : Alexandre T. Filippov

Download or read book The Versatile Soliton written by Alexandre T. Filippov and published by Springer Science & Business Media. This book was released on 2010-05-18 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this engaging book, the concept of the soliton is traced from the beginning of the last century to modern times with its recent applications.

Solitons

Author : P. G. Drazin
Publisher : Cambridge University Press
ISBN 13 : 0521274222
Total Pages : 149 pages
Book Rating : 4.5/5 (212 download)

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Book Synopsis Solitons by : P. G. Drazin

Download or read book Solitons written by P. G. Drazin and published by Cambridge University Press. This book was released on 1983-07-21 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 'soliton' is a localized nonlinear wave of permanent form which may interact strongly with other solitons so that when they separate after the interaction they regain their original forms. This textbook is an account of the theory of solitons and of the diverse applications of the theory to nonlinear systems arising in the physical sciences. The essence of the book is an introduction to the method of inverse scattering. Solitary waves, cnoidal waves, conservation laws, the initial-value problem for the Korteweg-de Vries equation, the Lax method, the sine-Gordon equation and Backlund transformations are treated. The book will be useful for research workers who wish to learn about solitons as well as graduate students in mathematics, physics and engineering.

Solitons in Physics, Mathematics, and Nonlinear Optics

Author : Peter J. Olver
Publisher : Springer Science & Business Media
ISBN 13 : 1461390338
Total Pages : 220 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Solitons in Physics, Mathematics, and Nonlinear Optics by : Peter J. Olver

Download or read book Solitons in Physics, Mathematics, and Nonlinear Optics written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications SOLITONS IN PHYSICS, MATHEMATICS, AND NONLINEAR OPTICS is based on the proceedings of two workshops which were an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshops focussed on the main parts of the theory of solitons and on the applications of solitons in physics, biology and engineering, with a special concentration on nonlinear optics. We thank the Coordinating Committee: James Glimm, Daniel Joseph, Barbara Keyfitz, An Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for drew planning and implementing the stimulating year-long program. We especially thank the Workshop Organizers for Solitons in Physics and Mathematics, Alan Newell, Peter Olver, and David Sattinger, and for Nonlinear Optics and Plasma Physics, David Kaup and Yuji Kodama for their efforts in bringing together many of the major figures in those research fields in which solitons in physics, mathematics, and nonlinear optics theories are used. A vner Friedman Willard Miller, Jr. PREFACE This volume includes some of the lectures given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 LM. A. year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry.

Solitons

Author : G. Eilenberger
Publisher : Springer Science & Business Media
ISBN 13 : 364281509X
Total Pages : 203 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Solitons by : G. Eilenberger

Download or read book Solitons written by G. Eilenberger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1.1 Why Study Solitons? The last century of physics, which was initiated by Maxwell's completion of the theory of electromagnetism, can, with some justification, be called the era of linear physi cs. ~Jith few excepti ons, the methods of theoreti ca 1 phys ics have been dominated by linear equations (Maxwell, Schrodinger), linear mathematical objects (vector spaces, in particular Hilbert spaces), and linear methods (Fourier transforms, perturbation theory, linear response theory) . Naturally the importance of nonlinearity, beginning with the Navier-Stokes equations and continuing to gravitation theory and the interactions of par ticles in solids, nuclei, and quantized fields, was recognized. However, it was hardly possible to treat the effects of nonlinearity, except as a per turbation to the basis solutions of the linearized theory. During the last decade, it has become more widely recognized in many areas of "field physics" that nonlinearity can result in qualitatively new phenom ena which cannot be constructed via perturbation theory starting from linear ized equations. By "field physics" we mean all those areas of theoretical physics for which the description of physical phenomena leads one to consider field equations, or partial differential equations of the form (1.1.1) ~t or ~tt = F(~, ~x ...) for one- or many-component "fields" Ht, x, y ...) (or their quantum analogs).