Solitons in Field Theory and Nonlinear Analysis

Solitons in Field Theory and Nonlinear Analysis

Author: Yisong Yang

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 571

ISBN-13: 1475765487

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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.


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.

Topological and Non-Topological Solitons in Scalar Field Theories

Topological and Non-Topological Solitons in Scalar Field Theories

Author: Yakov M. Shnir

Publisher: Cambridge University Press

Published: 2018-07-26

Total Pages: 281

ISBN-13: 1316997154

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Solitons emerge in various non-linear systems as stable localized configurations, behaving in many ways like particles, from non-linear optics and condensed matter to nuclear physics, cosmology and supersymmetric theories. This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, it brings together debates around solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples. These include the Kortenweg-de-Vries system, sine-Gordon model, kinks and oscillons, and skyrmions and hopfions. The classical field theory of scalar field in various spatial dimensions is used throughout the book in presentation of related concepts, both at the technical and conceptual level. Providing a comprehensive introduction to the description and construction of solitons, this book is ideal for researchers and graduate students in mathematics and theoretical physics.


Book Synopsis Topological and Non-Topological Solitons in Scalar Field Theories by : Yakov M. Shnir

Download or read book Topological and Non-Topological Solitons in Scalar Field Theories written by Yakov M. Shnir and published by Cambridge University Press. This book was released on 2018-07-26 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solitons emerge in various non-linear systems as stable localized configurations, behaving in many ways like particles, from non-linear optics and condensed matter to nuclear physics, cosmology and supersymmetric theories. This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, it brings together debates around solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples. These include the Kortenweg-de-Vries system, sine-Gordon model, kinks and oscillons, and skyrmions and hopfions. The classical field theory of scalar field in various spatial dimensions is used throughout the book in presentation of related concepts, both at the technical and conceptual level. Providing a comprehensive introduction to the description and construction of solitons, this book is ideal for researchers and graduate students in mathematics and theoretical physics.

Quantum Field Theory III: Gauge Theory

Quantum Field Theory III: Gauge Theory

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

Published: 2011-08-17

Total Pages: 1141

ISBN-13: 3642224210

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In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).


Book Synopsis Quantum Field Theory III: Gauge Theory by : Eberhard Zeidler

Download or read book Quantum Field Theory III: Gauge Theory written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2011-08-17 with total page 1141 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).

Soliton Theory and Its Applications

Soliton Theory and Its Applications

Author: Chaohao Gu

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 414

ISBN-13: 3662031027

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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.


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.

Methods in Nonlinear Analysis

Methods in Nonlinear Analysis

Author: Kung Ching Chang

Publisher: Springer Science & Business Media

Published: 2005-08-26

Total Pages: 462

ISBN-13: 9783540241331

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This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.


Book Synopsis Methods in Nonlinear Analysis by : Kung Ching Chang

Download or read book Methods in Nonlinear Analysis written by Kung Ching Chang and published by Springer Science & Business Media. This book was released on 2005-08-26 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.

Quantum Field Theory I: Basics in Mathematics and Physics

Quantum Field Theory I: Basics in Mathematics and Physics

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

Published: 2007-04-18

Total Pages: 1060

ISBN-13: 354034764X

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This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.


Book Synopsis Quantum Field Theory I: Basics in Mathematics and Physics by : Eberhard Zeidler

Download or read book Quantum Field Theory I: Basics in Mathematics and Physics written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2007-04-18 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Perspectives in Nonlinear Partial Differential Equations

Perspectives in Nonlinear Partial Differential Equations

Author: Henri Berestycki

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 522

ISBN-13: 0821841904

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In celebration of Haim Brezis's 60th birthday, a conference was held at the Ecole Polytechnique in Paris, with a program testifying to Brezis's wide-ranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges.


Book Synopsis Perspectives in Nonlinear Partial Differential Equations by : Henri Berestycki

Download or read book Perspectives in Nonlinear Partial Differential Equations written by Henri Berestycki and published by American Mathematical Soc.. This book was released on 2007 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: In celebration of Haim Brezis's 60th birthday, a conference was held at the Ecole Polytechnique in Paris, with a program testifying to Brezis's wide-ranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges.

Solitons And Particles

Solitons And Particles

Author: Giulio Soliani

Publisher: World Scientific

Published: 1984-12-01

Total Pages: 837

ISBN-13: 9814513504

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This is the most up-to-date book on solitons and is divided into two parts. Part 1: Detailed introductory lectures on different aspects of solitons plus lectures on the mathematical aspects on this subject. Part 2: Is a collection of reprints on mathematical theories of solitons, solitons in field theory, solitons as particles and their properties, especially topological and physical properties. This book is aimed at a wide audience of physicists and mathematicians. It is an ideal reference book for young researchers and graduate students.


Book Synopsis Solitons And Particles by : Giulio Soliani

Download or read book Solitons And Particles written by Giulio Soliani and published by World Scientific. This book was released on 1984-12-01 with total page 837 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the most up-to-date book on solitons and is divided into two parts. Part 1: Detailed introductory lectures on different aspects of solitons plus lectures on the mathematical aspects on this subject. Part 2: Is a collection of reprints on mathematical theories of solitons, solitons in field theory, solitons as particles and their properties, especially topological and physical properties. This book is aimed at a wide audience of physicists and mathematicians. It is an ideal reference book for young researchers and graduate students.

MEAN FIELD THEORIES AND DUAL VARIATION

MEAN FIELD THEORIES AND DUAL VARIATION

Author: Takashi Suzuki

Publisher: Springer Science & Business Media

Published: 2009-01-01

Total Pages: 299

ISBN-13: 9491216228

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A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality” according to the PDE weak solutions and “hierarchy” for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski–Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.


Book Synopsis MEAN FIELD THEORIES AND DUAL VARIATION by : Takashi Suzuki

Download or read book MEAN FIELD THEORIES AND DUAL VARIATION written by Takashi Suzuki and published by Springer Science & Business Media. This book was released on 2009-01-01 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality” according to the PDE weak solutions and “hierarchy” for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski–Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.

Variational Methods in Nonlinear Field Equations

Variational Methods in Nonlinear Field Equations

Author: Vieri Benci

Publisher: Springer

Published: 2014-10-24

Total Pages: 253

ISBN-13: 3319069144

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The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.


Book Synopsis Variational Methods in Nonlinear Field Equations by : Vieri Benci

Download or read book Variational Methods in Nonlinear Field Equations written by Vieri Benci and published by Springer. This book was released on 2014-10-24 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.