Aspects Of Integrability Of Differential Systems And Fields
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Aspects Of Integrability Of Differential Systems And Fields
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Author : Costas J. Papachristou
language : en
Publisher: Springer Nature
Release Date : 2020-01-01
Aspects Of Integrability Of Differential Systems And Fields written by Costas J. Papachristou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-01 with Science categories.
This book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields. The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and engineering. The following general cases of integrability are examined: (a) path-independence of line integrals of vector fields on the plane and in space; (b) integration of a system of ordinary differential equations by using first integrals; and (c) integrable systems of partial differential equations. Special topics include the integration of analytic functions and some elements from the geometric theory of differential systems. Certain more advanced subjects, such as Lax pairs and Bäcklund transformations, are also discussed. The book is written at an intermediate level for educational purposes. The presentation is as simple as the topics allow, often sacrificing mathematical rigor in favor of pedagogical efficiency.
Algebraic Aspects Of Darboux Transformations Quantum Integrable Systems And Supersymmetric Quantum Mechanics
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Author : Primitivo B. Acosta Humanez
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Algebraic Aspects Of Darboux Transformations Quantum Integrable Systems And Supersymmetric Quantum Mechanics written by Primitivo B. Acosta Humanez 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 2012 with Mathematics categories.
This volume represents the 2010 Jairo Charris Seminar in Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, which was held at the Universidad Sergio Arboleda in Santa Marta, Colombia. The papers cover the fields of Supersymmetric Quantum Mechanics and Quantum Integrable Systems, from an algebraic point of view. Some results presented in this volume correspond to the analysis of Darboux Transformations in higher order as well as some exceptional orthogonal polynomials. The reader will find an interesting Galois approach to study finite gap potentials. This book is published in cooperation with Instituto de Matematicas y sus Aplicaciones (IMA).
Aspects Of Integrability Of Differential Systems And Fields
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Author : Costas J. Papachristou
language : en
Publisher: Springer
Release Date : 2020-01-02
Aspects Of Integrability Of Differential Systems And Fields written by Costas J. Papachristou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-02 with Science categories.
This book serves as an introduction to the concept of integrability as it applies to systems of differential equations as well as to vector-valued fields. The author focuses on specific aspects of integrability that are often encountered in a variety of problems in applied mathematics, physics and engineering. The following general cases of integrability are examined: (a) path-independence of line integrals of vector fields on the plane and in space; (b) integration of a system of ordinary differential equations by using first integrals; and (c) integrable systems of partial differential equations. Special topics include the integration of analytic functions and some elements from the geometric theory of differential systems. Certain more advanced subjects, such as Lax pairs and Bäcklund transformations, are also discussed. The book is written at an intermediate level for educational purposes. The presentation is as simple as the topics allow, often sacrificing mathematical rigor in favor of pedagogical efficiency.
Continuous Symmetries And Integrability Of Discrete Equations
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Author : Decio Levi
language : en
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
Release Date : 2023-01-23
Continuous Symmetries And Integrability Of Discrete Equations written by Decio Levi and has been published by American Mathematical Society, Centre de Recherches Mathématiques this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-23 with Mathematics categories.
This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.
Side Iii Symmetries And Integrability Of Difference Equations
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Author : D. Levi
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Side Iii Symmetries And Integrability Of Difference Equations written by D. Levi 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 2000 with Mathematics categories.
This volume contains the proceedings of the third meeting on "Symmetries and Integrability of Difference Equations" (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art. Research in the field of difference equations-often referred to more generally as discrete systems-has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lie-type symmetries of differential-difference and difference-difference equations, integrability of fully discrete systems such as cellular automata, the connection between integrability and discrete geometry, the isomonodromy approach to discrete spectral problems and related discrete Painlevé equations, difference and q-difference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discrete-time dynamical systems. The proceedings will be valuable to mathematicians and theoretical physicists interested in the mathematical aspects and/or in the physical applications of discrete nonlinear dynamics, with special emphasis on the systems that can be integrated by analytic methods or at least admit special explicit solutions. The research in this volume will also be of interest to engineers working in discrete dynamics as well as to theoretical biologists and economists.
Symmetries And Integrability Of Difference Equations
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Author : Peter A. Clarkson
language : en
Publisher: Cambridge University Press
Release Date : 1999-02-04
Symmetries And Integrability Of Difference Equations written by Peter A. Clarkson 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 1999-02-04 with Mathematics categories.
This volume comprises state-of-the-art articles in discrete integrable systems.
Integrable Systems Quantum Groups And Quantum Field Theories
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Author : Alberto Ibort
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Systems Quantum Groups And Quantum Field Theories written by Alberto Ibort 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 many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.
The Einstein Equations And The Large Scale Behavior Of Gravitational Fields
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Author : Piotr T. Chrusciel
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Einstein Equations And The Large Scale Behavior Of Gravitational Fields written by Piotr T. Chrusciel 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 Science categories.
The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.
Classical And Quantum Nonlinear Integrable Systems
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Author : A Kundu
language : en
Publisher: CRC Press
Release Date : 2019-04-23
Classical And Quantum Nonlinear Integrable Systems written by A Kundu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-23 with Science categories.
Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories
Hamiltonian Systems And Their Integrability
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Author : Mich'le Audin
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Hamiltonian Systems And Their Integrability written by Mich'le Audin 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 2008 with Mathematics categories.
Hamiltonian systems began as a mathematical approach to the study of mechanical systems. As the theory developed, it became clear that the systems that had a sufficient number of conserved quantities enjoyed certain remarkable properties. These are the completely integrable systems. In time, a rich interplay arose between integrable systems and other areas of mathematics, particularly topology, geometry, and group theory.This book presents some modern techniques in the theory of integrable systems viewed as variations on the theme of action-angle coordinates. These techniques include analytical methods coming from the Galois theory of differential equations, as well as more classical algebro-geometric methods related to Lax equations. Audin has included many examples and exercises. Most of the exercises build on the material in the text. None of the important proofs have been relegated to the exercises. Many of the examples are classical, rather than abstract. This book would be suitable for a graduate course in Hamiltonian systems.