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.
Download or read book Algebraic Aspects of Darboux Transformations Quantum Integrable Systems and Supersymmetric Quantum Mechanics written by Primitivo B. Acosta Humanez and published by American Mathematical Soc.. This book was released on 2012 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
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:
Download or read book B cklund 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.
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.
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 367 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
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.
Download or read book Bilinear Integrable Systems from Classical to Quantum Continuous to Discrete written by Ludwig Faddeev and published by Springer Science & Business Media. This book was released on 2007-05-16 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: On April 29, 1814 Napoleon landed on the island of Elba, surrounded with a personal army of 1200 men. The allies, Russia, Prussia, England and Austria, hadforcedhimintoexileafteranumberofverycostlydefeats;hewasdeprived ofallhistitles, butcouldkeepthetitleof"EmperorofElba". Historytellsusthat each morning he took long walks in the sun, reviewed his army each midday anddiscussedworldmatterswithnewlyappointedadvisors, followingthesame pattern everyday, to the great surprise of Campbell, the British of?cer who was to keep an eye on him. All this made everyone believe he was settled there for good. Napoleononcesaid:Elbaisbeautiful, butabitsmall. Elbawasde?nitely a source of inspiration; indeed, the early morning, March 6, 1815, Metternich, the chancellor of Austria was woken up by one of his aides with the stunning news that Napoleon had left Elba with his 1200 men and was marching to Paris with little resistance; A few days later he took up his throne again in the Tuileries. In spite of his insatiable hunger for battles and expansion, he is remembered as an important statesman. He was a pioneer in setting up much of the legal, administrative and political machinery in large parts of continental Europe. We gathered here in a lovely and quaint?shing port, Marciana Marina on theislandofElba, tocelebrateoneofthepioneersofintegrablesystems, Hirota Sensei, andthisattheoccasionofhisseventiethbirthday. Trainedasaphysicist in his home university Kyushu University, Professor Hirota earned his PhD in '61 at Northwestern University with Professor Siegert in the?eld of "Quantum Statistical mechanics". He wrote a widely appreciated Doctoral dissertation on "FunctionalIntegralrepresentationofthegrandpartitionfunction."
Download or read book Integrability written by Alexander Mikhailov and published by Springer Science & Business Media. This book was released on 2008-11-25 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of the book is to give a comprehensive account of the variety of approaches to such an important and complex concept as Integrability. Dev- oping mathematical models, physicists often raise the following questions: whether the model obtained is integrable or close in some sense to an integrable one and whether it can be studied in depth analytically. In this book we have tried to c- ate a mathematical framework to address these issues, and we give descriptions of methods and review results. In the Introduction we give a historical account of the birth and development of the theory of integrable equations, focusing on the main issue of the book – the concept of integrability itself. A universal de nition of Integrability is proving to be elusive despite more than 40 years of its development. Often such notions as “- act solvability” or “regular behaviour” of solutions are associated with integrable systems. Unfortunately these notions do not lead to any rigorous mathematical d- inition. A constructive approach could be based upon the study of hidden and rich algebraic or analytic structures associated with integrable equations. The requi- ment of existence of elements of these structures could, in principle, be taken as a de nition for integrability. It is astonishing that the nal result is not sensitive to the choice of the structure taken; eventually we arrive at the same pattern of eq- tions.
Download or read book Algebraic and Geometric Aspects of Integrable Systems and Random Matrices written by Anton Dzhamay and published by American Mathematical Soc.. This book was released on 2013-06-26 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates
Download or read book B cklund 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.
Download or read book B cklund 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.
Download or read book Symmetries and Integrability of Difference Equations written by Decio Levi and published by Springer. This book was released on 2017-06-30 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.
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:
Download or read book Quantum Integrable Systems written by Asesh Roy Chowdhury and published by CRC Press. This book was released on 2004-01-28 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
Download or read book Discrete Integrable Systems written by Basil Grammaticos and published by Springer. This book was released on 2004-06-22 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of a set of ten lectures conceived as both introduction and up-to-date survey on discrete integrable systems. It constitutes a companion book to "Integrability of Nonlinear Systems" (Springer-Verlag, 2004, LNP 638, ISBN 3-540-20630-2). Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.
Download or read book Integrable Systems Geometry and Topology written by Chuu-lian Terng and published by American Mathematical Soc.. This book was released on with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. The article by Burstall gives a beautiful exposition on isothermic surfaces and the
