Darboux Transformations And 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.

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

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

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.

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).

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.

Rogue Waves In Integrable Systems

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Author : Bo Yang
language : en
Publisher: Springer Nature
Release Date : 2024-10-21

Rogue Waves In Integrable Systems written by Bo Yang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-21 with Science categories.

This book offers a holistic picture of rogue waves in integrable systems. Rogue waves are a rare but extreme phenomenon that occur most famously in water, but also in other diverse contexts such as plasmas, optical fibers and Bose-Einstein condensates where, despite the seemingly disparate settings, a common theoretical basis exists. This book presents the physical derivations of the underlying integrable nonlinear partial differential equations, derives the explicit and compact rogue wave solutions in these integrable systems, and analyzes rogue wave patterns that arise in these solutions, for many integrable systems and in multiple physical contexts. Striking a balance between theory and experiment, the book also surveys recent experimental insights into rogue waves in water, optical fibers, plasma, and Bose-Einstein condensates. In taking integrable nonlinear wave systems as a starting point, this book will be of interest to a broad cross section of researchers and graduate students in physics and applied mathematics who encounter nonlinear waves.

Integrable Systems From Classical To Quantum

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Author : John P. Harnad
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Integrable Systems From Classical To Quantum written by John P. Harnad 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 2000 with Mathematics categories.

This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in r s3risingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a nice cross-section of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an up-to-date introduction and an overview of many of the main areas of study in the theory of integral systems.