Darboux Transformations In Integrable Systems

Author : Chaohao Gu,Anning Hu,Zixiang Zhou
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 43,6 Mb
Release : 2006-07-09
Category : Science
ISBN : 9781402030888

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Darboux Transformations in Integrable Systems by Chaohao Gu,Anning Hu,Zixiang Zhou Pdf

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.

Author : Primitivo B. Acosta Humanez
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 40,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821875841

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Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics by Primitivo B. Acosta Humanez Pdf

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).

Author : Basil Grammaticos,Yvette Kosmann-Schwarzbach,Thamizharasi Tamizhmani
Publisher : Unknown
Page : 460 pages
File Size : 53,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662144603

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Discrete Integrable Systems by Basil Grammaticos,Yvette Kosmann-Schwarzbach,Thamizharasi Tamizhmani Pdf

Author : C. Rogers,W. K. Schief
Publisher : Cambridge University Press
Page : 436 pages
File Size : 55,8 Mb
Release : 2002-06-24
Category : Mathematics
ISBN : 0521012880

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Bäcklund and Darboux Transformations by C. Rogers,W. K. Schief Pdf

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.

Author : Ludwig Faddeev,Pierre Van Moerbeke,Franklin Lambert
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 55,5 Mb
Release : 2007-05-16
Category : Science
ISBN : 9781402035036

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Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete by Ludwig Faddeev,Pierre Van Moerbeke,Franklin Lambert Pdf

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."

Author : A. A. Coley
Publisher : American Mathematical Soc.
Page : 458 pages
File Size : 44,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821828038

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Bäcklund and Darboux Transformations by A. A. Coley Pdf

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.

Author : Norbert Euler,Da-jun Zhang
Publisher : CRC Press
Page : 367 pages
File Size : 48,7 Mb
Release : 2021-09-07
Category : Mathematics
ISBN : 9781000423303

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Nonlinear Systems and Their Remarkable Mathematical Structures by Norbert Euler,Da-jun Zhang Pdf

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

Author : A. A. Coley
Publisher : American Mathematical Soc.
Page : 460 pages
File Size : 46,9 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 0821870254

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Bäcklund and Darboux Transformations by A. A. Coley Pdf

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.

Author : Anton Dzhamay,Ken'ichi Maruno,Virgil U. Pierce
Publisher : American Mathematical Soc.
Page : 363 pages
File Size : 51,6 Mb
Release : 2013-06-26
Category : Mathematics
ISBN : 9780821887479

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Algebraic and Geometric Aspects of Integrable Systems and Random Matrices by Anton Dzhamay,Ken'ichi Maruno,Virgil U. Pierce Pdf

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

Author : J. Hietarinta,N. Joshi,F. W. Nijhoff
Publisher : Cambridge University Press
Page : 461 pages
File Size : 51,5 Mb
Release : 2016-09
Category : Mathematics
ISBN : 9781107042728

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Discrete Systems and Integrability by J. Hietarinta,N. Joshi,F. W. Nijhoff Pdf

A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Author : Decio Levi,Raphaël Rebelo,Pavel Winternitz
Publisher : Springer
Page : 435 pages
File Size : 50,9 Mb
Release : 2017-06-30
Category : Science
ISBN : 9783319566665

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Symmetries and Integrability of Difference Equations by Decio Levi,Raphaël Rebelo,Pavel Winternitz Pdf

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.

Author : Basil Grammaticos,Yvette Kosmann-Schwarzbach,Thamizharasi Tamizhmani
Publisher : Springer
Page : 472 pages
File Size : 52,9 Mb
Release : 2004-06-22
Category : Science
ISBN : 3540214259

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Discrete Integrable Systems by Basil Grammaticos,Yvette Kosmann-Schwarzbach,Thamizharasi Tamizhmani Pdf

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.

Author : Alfinito Eleonora,Boiti M,Martina Luigi
Publisher : World Scientific
Page : 628 pages
File Size : 43,6 Mb
Release : 1996-06-20
Category : Electronic
ISBN : 9789814548120

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Nonlinear Physics: Theory And Experiment : Nature, Structure And Properties Of Nonlinear Phenomena - Proceedings Of The First Conference by Alfinito Eleonora,Boiti M,Martina Luigi Pdf

Author : Alexander Mikhailov
Publisher : Springer
Page : 339 pages
File Size : 44,8 Mb
Release : 2008-11-05
Category : Science
ISBN : 9783540881117

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Integrability by Alexander Mikhailov Pdf

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.

Author : Vladimir Gerdjikov,Gaetano Vilasi,Alexandar Borisov Yanovski
Publisher : Springer
Page : 643 pages
File Size : 45,9 Mb
Release : 2008-12-02
Category : Science
ISBN : 9783540770541

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Integrable Hamiltonian Hierarchies by Vladimir Gerdjikov,Gaetano Vilasi,Alexandar Borisov Yanovski Pdf

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.