Darboux Transformations In Integrable Systems

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Darboux Transformations in Integrable Systems

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Author : Chaohao Gu
Publisher : Springer Science & Business Media
ISBN 13 : 1402030886
Total Pages : 317 pages
Book Rating : 4.4/5 (2 download)

Book Synopsis Darboux Transformations in Integrable Systems by : Chaohao Gu

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.

Discrete Integrable Systems

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Author : Basil Grammaticos
Publisher :
ISBN 13 : 9783662144602
Total Pages : 460 pages
Book Rating : 4.1/5 (446 download)

Book Synopsis Discrete Integrable Systems by : Basil Grammaticos

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:

Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics

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Author : Primitivo B. Acosta Humanez
Publisher : American Mathematical Soc.
ISBN 13 : 0821875841
Total Pages : 226 pages
Book Rating : 4.8/5 (218 download)

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

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).

Bäcklund and Darboux Transformations

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Author : C. Rogers
Publisher : Cambridge University Press
ISBN 13 : 9780521012881
Total Pages : 436 pages
Book Rating : 4.0/5 (128 download)

Book Synopsis Bäcklund and Darboux Transformations by : C. Rogers

Download or read book Bäcklund 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.

Discrete Systems and Integrability

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Author : J. Hietarinta
Publisher : Cambridge University Press
ISBN 13 : 1107042720
Total Pages : 461 pages
Book Rating : 4.1/5 (7 download)

Book Synopsis Discrete Systems and Integrability by : J. Hietarinta

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.

Constrained Willmore Surfaces

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Author : Áurea Casinhas Quintino
Publisher : Cambridge University Press
ISBN 13 : 1108794424
Total Pages : 261 pages
Book Rating : 4.1/5 (87 download)

Book Synopsis Constrained Willmore Surfaces by : Áurea Casinhas Quintino

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.

Darboux Transformations and Solitons

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Author : Vladimir B. Matveev
Publisher : Springer
ISBN 13 : 9783662009246
Total Pages : 122 pages
Book Rating : 4.0/5 (92 download)

Book Synopsis Darboux Transformations and Solitons by : Vladimir B. Matveev

Download or read book Darboux Transformations and Solitons written by Vladimir B. Matveev and published by Springer. This book was released on 1992-09-30 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modem theory of solitons was born in 1967 when Gardner, Greene, Kruskal and Miura related the solution of the Cauchy initial value problem for the Korteweg-de Vries equation to the inverse scattering problem for a one dimensional linear Schrödinger equation. Soliton theory is now a large part of theoretical and mathematical physics. An important method used to solve related equations is based on the Inverse Scattering Transform (IST). This IST method has been extended and applied to a large variety of (analytically) solvable non linear evolution equations, including many important examples describing phe nomena in nonlinear optics, solid state physics, hydrodynamics, theory of general relativity, plasma physics, etc. In the about twenty years of development the necessary mathematical tools have become rather sophisticated. They include the methods of algebraic geome try, the machinery of group representations, the theory of the local and nonlocal Riemann-Hilbert problem and many other "higher" levels of contemporary math ematics.

Nonlinear Systems and Their Remarkable Mathematical Structures

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Author : Norbert Euler
Publisher : CRC Press
ISBN 13 : 1000423301
Total Pages : 367 pages
Book Rating : 4.0/5 (4 download)

Book Synopsis Nonlinear Systems and Their Remarkable Mathematical Structures by : Norbert Euler

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

Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete

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Author : Ludwig Faddeev
Publisher : Springer Science & Business Media
ISBN 13 : 1402035039
Total Pages : 394 pages
Book Rating : 4.4/5 (2 download)

Book Synopsis Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete by : Ludwig Faddeev

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."

Integrable And Superintegrable Systems

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Author : Boris A Kuperschmidt
Publisher : World Scientific
ISBN 13 : 9814506737
Total Pages : 399 pages
Book Rating : 4.8/5 (145 download)

Book Synopsis Integrable And Superintegrable Systems by : Boris A Kuperschmidt

Download or read book Integrable And Superintegrable Systems written by Boris A Kuperschmidt and published by World Scientific. This book was released on 1990-10-25 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.

Algebraic and Geometric Aspects of Integrable Systems and Random Matrices

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Author : Anton Dzhamay
Publisher : American Mathematical Soc.
ISBN 13 : 0821887475
Total Pages : 363 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Algebraic and Geometric Aspects of Integrable Systems and Random Matrices by : Anton Dzhamay

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

Symmetries and Integrability of Difference Equations

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Author : Decio Levi
Publisher : Springer
ISBN 13 : 3319566660
Total Pages : 441 pages
Book Rating : 4.3/5 (195 download)

Book Synopsis Symmetries and Integrability of Difference Equations by : Decio Levi

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 441 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.

Two Reports on Harmonic Maps

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Author : James Eells
Publisher : World Scientific
ISBN 13 : 9789810214661
Total Pages : 38 pages
Book Rating : 4.2/5 (146 download)

Book Synopsis Two Reports on Harmonic Maps by : James Eells

Download or read book Two Reports on Harmonic Maps written by James Eells and published by World Scientific. This book was released on 1995 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, å-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Khlerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers.

Integrability and Nonintegrability of Dynamical Systems

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Author : Alain Goriely
Publisher : World Scientific
ISBN 13 : 981023533X
Total Pages : 435 pages
Book Rating : 4.8/5 (12 download)

Book Synopsis Integrability and Nonintegrability of Dynamical Systems by : Alain Goriely

Download or read book Integrability and Nonintegrability of Dynamical Systems written by Alain Goriely and published by World Scientific. This book was released on 2001 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book examines qualitative and quantitative methods for nonlinear differential equations, as well as integrability and nonintegrability theory. Starting from the idea of a constant of motion for simple systems of differential equations, it investigates the essence of integrability, its geometrical relevance and dynamical consequences. Integrability theory is approached from different perspectives, first in terms of differential algebra, then in terms of complex time singularities and finally from the viewpoint of phase geometry (for both Hamiltonian and non-Hamiltonian systems). As generic systems of differential equations cannot be exactly solved, the book reviews the different notions of nonintegrability and shows how to prove the nonexistence of exact solutions and/or a constant of motion. Finally, nonintegrability theory is linked to dynamical systems theory by showing how the property of complete integrability, partial integrability or nonintegrability can be related to regular and irregular dynamics in phase space.

Introduction to Classical Integrable Systems

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Author : Olivier Babelon
Publisher : Cambridge University Press
ISBN 13 : 9780521822671
Total Pages : 622 pages
Book Rating : 4.8/5 (226 download)

Book Synopsis Introduction to Classical Integrable Systems by : Olivier Babelon

Download or read book Introduction to Classical Integrable Systems written by Olivier Babelon and published by Cambridge University Press. This book was released on 2003-04-17 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.

Nonlinear Physics: Theory And Experiment : Nature, Structure And Properties Of Nonlinear Phenomena - Proceedings Of The First Conference

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Author : Eleonora Alfinito
Publisher : World Scientific
ISBN 13 : 981454812X
Total Pages : 630 pages
Book Rating : 4.8/5 (145 download)

Book Synopsis Nonlinear Physics: Theory And Experiment : Nature, Structure And Properties Of Nonlinear Phenomena - Proceedings Of The First Conference by : Eleonora Alfinito

Download or read book Nonlinear Physics: Theory And Experiment : Nature, Structure And Properties Of Nonlinear Phenomena - Proceedings Of The First Conference written by Eleonora Alfinito and published by World Scientific. This book was released on 1996-06-20 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the Workshop 'Nonlinear Physics. Theory and Experiment' held in Gallipoli (Lecce, Italy) from June 29 to July 7, 1995.The purpose of the Workshop was to bring together scientists whose common interest is the nature, structure and properties of nonlinear phenomena in various areas of physics and applied mathematics.The purpose of the Workshop was to bring together scientists whose common interest is the nature, structure and properties of nonlinear phenomena in various areas of physics and applied mathematics.In fact, topics covered at the Workshop run from nonlinear optics to molecular dynamics, plasma waves, hydrodynamics, quantum electronics and solid state, and from inverse scattering transform methods to dynamical systems including integrability, hamiltonian structures, geometrical aspects, turbulence and chaos.

Solitons in Mathematics and Physics

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Author : Alan C. Newell
Publisher : SIAM
ISBN 13 : 0898711967
Total Pages : 259 pages
Book Rating : 4.8/5 (987 download)

Book Synopsis Solitons in Mathematics and Physics by : Alan C. Newell

Download or read book Solitons in Mathematics and Physics written by Alan C. Newell and published by SIAM. This book was released on 1985-06-01 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of the soliton, focusing on the properties that make it physically ubiquitous and the soliton equation mathematically miraculous.