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Darboux Transformations And Solitons
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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.
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:
Book Synopsis Darboux Transformations and Solitons by : Vladimir B. Matveev
Download or read book Darboux Transformations and Solitons written by Vladimir B. Matveev and published by Springer. This book was released on 1992-09-30 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modem theory of solitons was born in 1967 when Gardner, Greene, Kruskal and Miura related the solution of the Cauchy initial value problem for the Korteweg-de Vries equation to the inverse scattering problem for a one dimensional linear Schrödinger equation. Soliton theory is now a large part of theoretical and mathematical physics. An important method used to solve related equations is based on the Inverse Scattering Transform (IST). This IST method has been extended and applied to a large variety of (analytically) solvable non linear evolution equations, including many important examples describing phe nomena in nonlinear optics, solid state physics, hydrodynamics, theory of general relativity, plasma physics, etc. In the about twenty years of development the necessary mathematical tools have become rather sophisticated. They include the methods of algebraic geome try, the machinery of group representations, the theory of the local and nonlocal Riemann-Hilbert problem and many other "higher" levels of contemporary math ematics.
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.
Book Synopsis Proceedings of the Workshop on Nonlinearity, Integrability and All That--Twenty Years After NEEDS '79 by : M. Boiti
Download or read book Proceedings of the Workshop on Nonlinearity, Integrability and All That--Twenty Years After NEEDS '79 written by M. Boiti and published by World Scientific. This book was released on 2000 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems ? classical and quantum ? are considered.
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 317 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.
Book Synopsis Discrete and Continuous Nonlinear Schrödinger Systems by : M. J. Ablowitz
Download or read book Discrete and Continuous Nonlinear Schrödinger Systems written by M. J. Ablowitz and published by Cambridge University Press. This book was released on 2004 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.
Book Synopsis Nonlinear Waves by : Lokenath Debnath
Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Book Synopsis The Direct Method in Soliton Theory by : Ryogo Hirota
Download or read book The Direct Method in Soliton Theory written by Ryogo Hirota and published by Cambridge University Press. This book was released on 2004-07-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Account of method of solving soliton equations by the inventor of the method.
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.
Book Synopsis Nonlinear Dispersive Waves by : Mark J. Ablowitz
Download or read book Nonlinear Dispersive Waves written by Mark J. Ablowitz and published by Cambridge University Press. This book was released on 2011-09-08 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
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.
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 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ba?cklund Transformations and Their Applications
Book Synopsis Integrable And Superintegrable Systems by : Boris A Kuperschmidt
Download or read book Integrable And Superintegrable Systems written by Boris A Kuperschmidt and published by World Scientific. This book was released on 1990-10-25 with total page 399 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 The Problem of Integrable Discretization by : Yuri B. Suris
Download or read book The Problem of Integrable Discretization written by Yuri B. Suris and published by Birkhäuser. This book was released on 2012-12-06 with total page 1078 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.
Book Synopsis Spectral and Dynamical Stability of Nonlinear Waves by : Todd Kapitula
Download or read book Spectral and Dynamical Stability of Nonlinear Waves written by Todd Kapitula and published by Springer Science & Business Media. This book was released on 2013-06-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability.
Book Synopsis Discrete Systems and Integrability by : J. Hietarinta
Download or read book Discrete Systems and Integrability written by J. Hietarinta and published by Cambridge University Press. This book was released on 2016-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.
