Darboux Transformations In Integrable Systems
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Darboux Transformations In Integrable Systems
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Author : Chaohao Gu
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-12-08
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 2004-12-08 with Mathematics 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.
Darboux Transformations And Integrable Systems
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Author : Vladimir B. Matveev
language : en
Publisher:
Release Date : 1996
Darboux Transformations And Integrable Systems written by Vladimir B. Matveev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Algebraic Aspects Of Darboux Transformations Quantum Integrable Systems And Supersymmetric Quantum Mechanics
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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).
Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices
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Author : Anton Dzhamay
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-26
Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices written by Anton Dzhamay 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 2013-06-26 with Mathematics categories.
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
Nonlinear Systems And Their Remarkable Mathematical Structures
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Author : Norbert Euler
language : en
Publisher: CRC Press
Release Date : 2021-09-07
Nonlinear Systems And Their Remarkable Mathematical Structures written by Norbert Euler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-07 with Mathematics categories.
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
Integrable Systems Nankai Lectures On Mathematical Physics 1987
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Author : Xing-chang Song
language : en
Publisher: World Scientific
Release Date : 1989-11-01
Integrable Systems Nankai Lectures On Mathematical Physics 1987 written by Xing-chang Song and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-11-01 with categories.
This workshop is part of a series of annual workshops organised by the Nankai Institute of Mathematics. Prominent scientists from abroad are invited to deliver the main lectures.
Integrable Systems Geometry And Topology
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Author : Chuu-lian Terng
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
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 2006 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. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and theirrelations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu,and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of Yang-Mills-Higgs equations on Riemann surfaces. The article by Terng and Uhlenbeck explains the gauge equivalence of the matrix non-linear Schrödinger equation, the Schrödinger flow on Grassmanian, and the Heisenberg Feromagnetic model. The bookprovides an introduction to integrable systems and their relation to differential geometry. It is suitable for advanced graduate students and research mathematicians. Information for our distributors: Titles in this series are copublished with International Press, Cambridge, MA.
Integrable Hamiltonian Hierarchies
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Author : Vladimir Gerdjikov
language : en
Publisher: Springer
Release Date : 2008-12-02
Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-02 with Science categories.
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.
Bilinear Integrable Systems From Classical To Quantum Continuous To Discrete
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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."
Symmetries And Integrability Of Difference Equations
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Author : Decio Levi
language : en
Publisher: Springer
Release Date : 2017-06-30
Symmetries And Integrability Of Difference Equations written by Decio Levi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-30 with Science categories.
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.