Backlund And Darboux Transformations

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Bäcklund and Darboux Transformations

Author : C. Rogers
Publisher : Cambridge University Press
ISBN 13 : 9780521012881
Total Pages : 436 pages
Book Rating : 4.0/5 (128 download)

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Book Synopsis Bäcklund and Darboux Transformations by : C. Rogers

Download or read book Bäcklund and Darboux Transformations written by C. Rogers and published by Cambridge University Press. This book was released on 2002-06-24 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the deep and fascinating connections that exist between a ubiquitous class of physically important waves known as solitons and the theory of transformations of a privileged class of surfaces as they were studied by eminent geometers of the nineteenth century. Thus, nonlinear equations governing soliton propagation and also mathematical descriptions of their remarkable interaction properties are shown to arise naturally out of the classical differential geometry of surfaces and what are termed Bäcklund-Darboux transformations.This text, the first of its kind, is written in a straightforward manner and is punctuated by exercises to test the understanding of the reader. It is suitable for use in higher undergraduate or graduate level courses directed at applied mathematicians or mathematical physics.

Bäcklund and Darboux Transformations

Author : A. A. Coley
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870259
Total Pages : 460 pages
Book Rating : 4.8/5 (72 download)

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Book Synopsis Bäcklund and Darboux Transformations by : A. A. Coley

Download or read book Bäcklund and Darboux Transformations written by A. A. Coley and published by American Mathematical Soc.. This book was released on 2001-01-01 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.

Darboux Transformations in Integrable Systems

Author : Chaohao Gu
Publisher : Springer Science & Business Media
ISBN 13 : 1402030886
Total Pages : 308 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Darboux Transformations in Integrable Systems by : Chaohao Gu

Download or read book Darboux Transformations in Integrable Systems written by Chaohao Gu and published by Springer Science & Business Media. This book was released on 2006-07-09 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry. This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years. Audience: The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics.

Bäcklund and Darboux Transformations

Author : A. A. Coley
Publisher : American Mathematical Soc.
ISBN 13 : 0821828037
Total Pages : 458 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Bäcklund and Darboux Transformations by : A. A. Coley

Download or read book Bäcklund and Darboux Transformations written by A. A. Coley and published by American Mathematical Soc.. This book was released on 2001 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a classical topic that has undergone rapid and fruitful development over the past 25 years, namely Backlund and Darboux transformations and their applications in the theory of integrable systems, also known as soliton theory. The book consists of two parts. The first is a series of introductory pedagogical lectures presented by leading experts in the field. They are devoted respectively to Backlund transformations of Painleve equations, to the dressing methodand Backlund and Darboux transformations, and to the classical geometry of Backlund transformations and their applications to soliton theory. The second part contains original contributions that represent new developments in the theory and applications of these transformations. Both the introductorylectures and the original talks were presented at an International Workshop that took place in Halifax, Nova Scotia (Canada). This volume covers virtually all recent developments in the theory and applications of Backlund and Darboux transformations.

Discrete Integrable Systems

Author : Basil Grammaticos
Publisher :
ISBN 13 : 9783662144602
Total Pages : 460 pages
Book Rating : 4.1/5 (446 download)

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Book Synopsis Discrete Integrable Systems by : Basil Grammaticos

Download or read book Discrete Integrable Systems written by Basil Grammaticos and published by . This book was released on 2014-01-15 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Constrained Willmore Surfaces

Author : Áurea Casinhas Quintino
Publisher : Cambridge University Press
ISBN 13 : 1108794424
Total Pages : 261 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Constrained Willmore Surfaces by : Áurea Casinhas Quintino

Download or read book Constrained Willmore Surfaces written by Áurea Casinhas Quintino and published by Cambridge University Press. This book was released on 2021-06-10 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Bäcklund to Darboux: a comprehensive journey through the transformation theory of constrained Willmore surfaces, with applications to constant mean curvature surfaces.

Nonlinear Physics: Theory And Experiment : Nature, Structure And Properties Of Nonlinear Phenomena - Proceedings Of The First Conference

Download Nonlinear Physics: Theory And Experiment : Nature, Structure And Properties Of Nonlinear Phenomena - Proceedings Of The First Conference PDF Online Free

Author : Alfinito Eleonora
Publisher : World Scientific
ISBN 13 : 981454812X
Total Pages : 628 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Nonlinear Physics: Theory And Experiment : Nature, Structure And Properties Of Nonlinear Phenomena - Proceedings Of The First Conference by : Alfinito Eleonora

Download or read book Nonlinear Physics: Theory And Experiment : Nature, Structure And Properties Of Nonlinear Phenomena - Proceedings Of The First Conference written by Alfinito Eleonora and published by World Scientific. This book was released on 1996-06-20 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantum Theory and Symmetries

Author : M. B. Paranjape
Publisher : Springer Nature
ISBN 13 : 3030557774
Total Pages : 670 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Quantum Theory and Symmetries by : M. B. Paranjape

Download or read book Quantum Theory and Symmetries written by M. B. Paranjape and published by Springer Nature. This book was released on 2021 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montreal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions. .

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.

Integrable Hamiltonian Hierarchies

Author : Vladimir Gerdjikov
Publisher : Springer
ISBN 13 : 3540770542
Total Pages : 643 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Integrable Hamiltonian Hierarchies by : Vladimir Gerdjikov

Download or read book Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and published by Springer. This book was released on 2008-12-02 with total page 643 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.

Inverse Problems and Nonlinear Evolution Equations

Author : Alexander L. Sakhnovich
Publisher : Walter de Gruyter
ISBN 13 : 3110258617
Total Pages : 354 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Inverse Problems and Nonlinear Evolution Equations by : Alexander L. Sakhnovich

Download or read book Inverse Problems and Nonlinear Evolution Equations written by Alexander L. Sakhnovich and published by Walter de Gruyter. This book was released on 2013-07-31 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.

Rogue and Shock Waves in Nonlinear Dispersive Media

Author : Miguel Onorato
Publisher : Springer
ISBN 13 : 331939214X
Total Pages : 370 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Rogue and Shock Waves in Nonlinear Dispersive Media by : Miguel Onorato

Download or read book Rogue and Shock Waves in Nonlinear Dispersive Media written by Miguel Onorato and published by Springer. This book was released on 2016-09-19 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.

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.

Ba?cklund Transformations and Their Applications

Author : Rogers
Publisher : Academic Press
ISBN 13 : 008095667X
Total Pages : 333 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Ba?cklund Transformations and Their Applications by : Rogers

Download or read book Ba?cklund Transformations and Their Applications written by Rogers and published by Academic Press. This book was released on 1982-06-18 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ba?cklund Transformations and Their Applications

Nonlinear Systems and Their Remarkable Mathematical Structures

Author : Norbert Euler
Publisher : CRC Press
ISBN 13 : 1000423263
Total Pages : 510 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Nonlinear Systems and Their Remarkable Mathematical Structures by : Norbert Euler

Download or read book Nonlinear Systems and Their Remarkable Mathematical Structures written by Norbert Euler and published by CRC Press. This book was released on 2021-09-07 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area . Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering Sciences. Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained.

Operator Theory, Analysis and the State Space Approach

Author : Harm Bart
Publisher : Springer
ISBN 13 : 3030042693
Total Pages : 464 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Operator Theory, Analysis and the State Space Approach by : Harm Bart

Download or read book Operator Theory, Analysis and the State Space Approach written by Harm Bart and published by Springer. This book was released on 2018-12-30 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Rien Kaashoek on the occasion of his 80th birthday and celebrates his many contributions to the field of operator theory during more than fifty years. In the first part of the volume, biographical information and personal accounts on the life of Rien Kaashoek are presented. Eighteen research papers by friends and colleagues of Rien Kaashoek are included in the second part. Contributions by J. Agler, Z.A. Lykova, N.J. Young, J.A. Ball, G.J. Groenewald, S. ter Horst, H. Bart, T. Ehrhardt, B. Silbermann, J.M. Bogoya, S.M. Grudsky, I.S. Malysheva, A. Böttcher, E. Wegert, Z. Zhou, Y. Eidelman, I. Haimovici, A.E. Frazho, A.C.M. Ran, B. Fritzsche, B. Kirstein, C.Madler, J. J. Jaftha, D.B. Janse van Rensburg, P. Junghanns, R. Kaiser, J. Nemcova, M. Petreczky, J.H. van Schuppen, L. Plevnik, P. Semrl, A. Sakhnovich, F.-O. Speck, S. Sremac, H.J. Woerdeman, H. Wolkowicz and N. Vasilevski.

Partially Integrable Evolution Equations in Physics

Author : R. Conte
Publisher : Springer Science & Business Media
ISBN 13 : 9400905912
Total Pages : 609 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Partially Integrable Evolution Equations in Physics by : R. Conte

Download or read book Partially Integrable Evolution Equations in Physics written by R. Conte and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the many physical phenomena ruled by partial differential equations, two extreme fields are currently overcrowded due to recent considerable developments: 1) the field of completely integrable equations, whose recent advances are the inverse spectral transform, the recursion operator, underlying Hamiltonian structures, Lax pairs, etc 2) the field of dynamical systems, often built as models of observed physical phenomena: turbulence, intermittency, Poincare sections, transition to chaos, etc. In between there is a very large region where systems are neither integrable nor nonintegrable, but partially integrable, and people working in the latter domain often know methods from either 1) or 2). Due to the growing interest in partially integrable systems, we decided to organize a meeting for physicists active or about to undertake research in this field, and we thought that an appropriate form would be a school. Indeed, some of the above mentioned methods are often adaptable outside their original domain and therefore worth to be taught in an interdisciplinary school. One of the main concerns was to keep a correct balance between physics and mathematics, and this is reflected in the list of courses.