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Soliton Equations And Hamiltonian Systems
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Book Synopsis Soliton Equations and Hamiltonian Systems by : L.A. Dickey
Download or read book Soliton Equations and Hamiltonian Systems written by L.A. Dickey and published by World Scientific. This book was released on 1991 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of soliton equations and integrable systems has developed rapidly during the last 20 years with numerous applications in mechanics and physics. For a long time books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this followed one single work by Gardner, Greene, Kruskal, and Miura about the Korteweg-de Vries equation (KdV) which, had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.
Book Synopsis Soliton Equations and Hamiltonian Systems by : L A Dickey
Download or read book Soliton Equations and Hamiltonian Systems written by L A Dickey and published by World Scientific. This book was released on 2003-01-17 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also because it satisfies the aesthetic need in a beautiful formula which is so inherent to mathematics. The second edition is up-to-date and differs from the first one considerably. One third of the book (five chapters) is completely new and the rest is refreshed and edited. Contents:Integrable Systems Generated by Linear Differential nth Order OperatorsHamiltonian StructuresHamiltonian Structure of the GD HierarchiesModified KdV and GD. The Kupershmidt–Wilson TheoremThe KP HierarchyBaker Function, τ-FunctionAdditional Symmetries, String EquationGrassmannian. Algebraic-Geometrical Krichever SolutionsMatrix First-Order Operator, AKNS-D HierarchyGeneralization of the AKNS-D Hierarchy: Single-Pole and Multi-Pole Matrix HierarchiesIsomonodromic Deformations and the Most General Matrix HierarchyTau Functions of Matrix HierarchiesKP, Modified KP, Constrained KP, Discrete KP, and q-KPAnother Chain of KP Hierarchies and Integrals Over Matrix VarietiesTransformational Properties of a Differential Operator under Diffeomorphisms and Classical W-AlgebrasFurther Restrictions of the KP, Stationary EquationsStationary Equations of the Matrix HierarchyField Lagrangian and Hamiltonian FormalismFurther Examples and Applications Readership: Applied mathematicians and mathematical physicists. Keywords:Integrable System;Soliton Equations;Hamiltonian Structure;Hierarchy of Equations;Baker Function;Ï-Function;Field Lagrangian FormalismReviews:“The author wrote in the introduction to the first edition that he 'tried to make this book available to beginners in this area having only basic training in algebra and analysis'. In the reviewer's opinion, he definitely achieved this goal. Moreover, this book can also be very useful for the researchers already active in the field of soliton equations and integrable systems.”Mathematical Reviews Reviews of the First Edition: “There is a bibliography of 112 items. This book is pedagogically written and is highly recommended for its detailed description of the resolvent method for soliton equations.”Mathematical Reviews “The book of L A Dickey presents one more point of view on the mathematical theory of solitons or, in other words, on the theory of nonlinear partial differential equations … The series of joint papers of I M Gelfand and L A Dickey in the middle of seventies was an important step in the development of the mathematical theory of nonlinear integrable equations … As a whole the book presents a very good exposition of the important part of the soliton theory.”Mathematics Abstracts
Book Synopsis Soliton Equations and Hamiltonian Systems by : Leonid A. Dickey
Download or read book Soliton Equations and Hamiltonian Systems written by Leonid A. Dickey and published by . This book was released on 1991 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Leonid A. Dickey Publisher :World Scientific Publishing Company Incorporated ISBN 13 :9789810202156 Total Pages :310 pages Book Rating :4.2/5 (21 download)
Book Synopsis Soliton Equations and Hamiltonian Systems by : Leonid A. Dickey
Download or read book Soliton Equations and Hamiltonian Systems written by Leonid A. Dickey and published by World Scientific Publishing Company Incorporated. This book was released on 1991 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of soliton equations and integrable systems has developed rapidly during the last 20 years with numerous applications in mechanics and physics. For a long time books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this followed one single work by Gardner, Greene, Kruskal, and Miura about the Korteweg-de Vries equation (KdV) which, had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. This branch of science is attractive because it is one of those which revives the interest in the basic principles of mathematics, a beautiful formula.
Book Synopsis Soliton Equations and Hamiltonian Systems by : Leonid A. Dickey
Download or read book Soliton Equations and Hamiltonian Systems written by Leonid A. Dickey and published by World Scientific. This book was released on 2003 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also because it satisfies the aesthetic need in a beautiful formula which is so inherent to mathematics. The second edition is up-to-date and differs from the first one considerably. One third of the book (five chapters) is completely new and the rest is refreshed and edited. Contents: Integrable Systems Generated by Linear Differential n th Order Operators; Hamiltonian Structures; Hamiltonian Structure of the GD Hierarchies; Modified KdV and GD. The KupershmidtOCoWilson Theorem; The KP Hierarchy; Baker Function, a-Function; Additional Symmetries, String Equation; Grassmannian. Algebraic-Geometrical Krichever Solutions; Matrix First-Order Operator, AKNS-D Hierarchy; Generalization of the AKNS-D Hierarchy: Single-Pole and Multi-Pole Matrix Hierarchies; Isomonodromic Deformations and the Most General Matrix Hierarchy; Tau Functions of Matrix Hierarchies; KP, Modified KP, Constrained KP, Discrete KP, and q -KP; Another Chain of KP Hierarchies and Integrals Over Matrix Varieties; Transformational Properties of a Differential Operator under Diffeomorphisms and Classical W -Algebras; Further Restrictions of the KP, Stationary Equations; Stationary Equations of the Matrix Hierarchy; Field Lagrangian and Hamiltonian Formalism; Further Examples and Applications. Readership: Applied mathematicians and mathematical physicists."
Book Synopsis Integrable Hamiltonian Hierarchies by : Vladimir Gerdjikov
Download or read book Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and published by Springer Science & Business Media. This book was released on 2008-06-02 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
Book Synopsis Nonlinear Integrable Equations by : Boris G. Konopelchenko
Download or read book Nonlinear Integrable Equations written by Boris G. Konopelchenko and published by Springer. This book was released on 1987-03-11 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hamiltonian Methods in the Theory of Solitons by : Ludwig Faddeev
Download or read book Hamiltonian Methods in the Theory of Solitons written by Ludwig Faddeev and published by Springer Science & Business Media. This book was released on 2007-08-10 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Download or read book Soliton Theory written by Allan P. Fordy and published by Manchester University Press. This book was released on 1990 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent introduction to the complete range of soliton theory including Hirota's method and Backlund transformations. Details physical applications of soliton theory with chapters on the peculiar wave patterns of the Andaman Sea, atmospheric phenomena, general relativity and Davydov solitons. Contains testing for full integrability, a discussion of the Painlevé technique, symmetries and conservation law.
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.
Book Synopsis Solitons and Chaos by : Ioannis Antoniou
Download or read book Solitons and Chaos written by Ioannis Antoniou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Solitons and Chaos" is a response to the growing interest in systems exhibiting these two complementary manifestations of nonlinearity. The papers cover a wide range of topics but share common mathematical notions and investigation techniques. An introductory note on eight concepts of integrability has been added as a guide for the uninitiated reader. Both specialists and graduate students will find this update on the state ofthe art useful. Key points: chaos vs. integrability; solitons: theory and applications; dissipative systems; Hamiltonian systems; maps and cascades; direct vs. inverse methods; higher dimensions; Lie groups, Painleve analysis, numerical algorithms; pertubation methods.
Book Synopsis Solitons and Geometry by : S. P. Novikov
Download or read book Solitons and Geometry written by S. P. Novikov and published by Cambridge University Press. This book was released on 1994-09-15 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to the geometry of Hamiltonian systems from the modern point of view where the basic structure is a Poisson bracket. Using this approach a mathematical analogue of the famous 'Dirac monopole' is obtained starting from the classical top in a gravity field. This approach is especially useful in physical applications in which a field theory appears; this is the subject of the second part of the lectures, which contains a theory of conservative hydrodynamic-type systems, based on Riemannian geometry, developed over the last decade. The theory has had success in solving problems in physics, such as ones associated with dispersive analogues of shock waves, and its development has led to the introduction of new notions in geometry. The book is based on lectures given by the author in Pisa and which were intended for a non-specialist audience. It provides an introduction from which to proceed to more advanced work in the area.
Book Synopsis Integrable and Superintegrable Systems by : Boris A. Kupershmidt
Download or read book Integrable and Superintegrable Systems written by Boris A. Kupershmidt and published by World Scientific. This book was released on 1990 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.
Book Synopsis Multi-Hamiltonian Theory of Dynamical Systems by : Maciej Blaszak
Download or read book Multi-Hamiltonian Theory of Dynamical Systems written by Maciej Blaszak and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a modern introduction to the Hamiltonian theory of dynamical systems, presenting a unified treatment of all types of dynamical systems, i.e., finite, lattice, and field. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system. As this property is closely related to integrability, this book presents an algebraic theory of integrable.
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.
Book Synopsis Important Developments in Soliton Theory by : A.S. Fokas
Download or read book Important Developments in Soliton Theory written by A.S. Fokas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.
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
