Darboux Transformations In Integrable Systems
DOWNLOAD
Download Darboux Transformations In Integrable Systems PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Darboux Transformations In Integrable Systems book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Darboux Transformations In Integrable Systems
DOWNLOAD
Author : Chaohao Gu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-09
Darboux Transformations In Integrable Systems written by Chaohao Gu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-09 with Science categories.
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.
Algebraic Aspects Of Darboux Transformations Quantum Integrable Systems And Supersymmetric Quantum Mechanics
DOWNLOAD
Author : Primitivo B. Acosta Humanez
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Algebraic Aspects Of Darboux Transformations Quantum Integrable Systems And Supersymmetric Quantum Mechanics written by Primitivo B. Acosta Humanez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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).
Integrability
DOWNLOAD
Author : Alexander Mikhailov
language : en
Publisher: Springer
Release Date : 2008-11-05
Integrability written by Alexander Mikhailov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-05 with Science categories.
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.
B Cklund And Darboux Transformations
DOWNLOAD
Author : A. A. Coley
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-01-01
B Cklund And Darboux Transformations written by A. A. Coley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
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.
B Cklund And Darboux Transformations
DOWNLOAD
Author : A. A. Coley
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
B Cklund And Darboux Transformations written by A. A. Coley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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
DOWNLOAD
Author : Basil Grammaticos
language : en
Publisher: Springer
Release Date : 2004-06-22
Discrete Integrable Systems written by Basil Grammaticos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-22 with Science categories.
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.
B Cklund And Darboux Transformations
DOWNLOAD
Author : C. Rogers
language : en
Publisher: Cambridge University Press
Release Date : 2002-06-24
B Cklund And Darboux Transformations written by C. Rogers and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-24 with Mathematics categories.
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.
Bilinear Integrable Systems From Classical To Quantum Continuous To Discrete
DOWNLOAD
Author : Ludwig Faddeev
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-16
Bilinear Integrable Systems From Classical To Quantum Continuous To Discrete written by Ludwig Faddeev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-16 with Science categories.
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."
Integrable Systems Geometry And Topology
DOWNLOAD
Author : Chuu-lian Terng
language : en
Publisher: American Mathematical Soc.
Release Date :
Integrable Systems Geometry And Topology written by Chuu-lian Terng and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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
Algebraic Aspects Of Integrable Systems
DOWNLOAD
Author : A.S. Fokas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Aspects Of Integrable Systems written by A.S. Fokas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A collection of articles in memory of Irene Dorfman and her research in mathematical physics. Among the topics covered are: the Hamiltonian and bi-Hamiltonian nature of continuous and discrete integrable equations; the t-function construction; the r-matrix formulation of integrable systems; pseudo-differential operators and modular forms; master symmetries and the Bocher theorem; asymptotic integrability; the integrability of the equations of associativity; invariance under Laplace-darboux transformations; trace formulae of the Dirac and Schrodinger periodic operators; and certain canonical 1-forms.