Overview

This Ergebnisse volume is aimed at a wide readership of mathematicians and physicists, graduate students and professionals. The main thrust of the book is to show how algebraic geometry, Lie theory and Painleve analysis can be used to explicitly solve integrable differential equations and construct the algebraic tori on which they linearize; at the same time, it is, for the student, a playing ground to applying algebraic geometry and Lie theory. The book is meant to be reasonably self-contained and presents numerous examples. The latter appear throughout the text to illustrate the ideas, and make up the core of the last part of the book. The first part of the book contains the basic tools from Lie groups, algebraic and differential geometry to understand the main topic.

Full Product Details

9783642061288

Table of Contents

Reviews

From the reviews of the first edition: The aim of this book is to explain `how algebraic geometry, Lie theory and Painleve analysis can be used to explicitly solve integrable differential equations'. ... One of the main advantages of this book is that the authors ... succeeded to present the material in a self-contained manner with numerous examples. As a result it can be also used as a reference book for many subjects in mathematics. In summary ... a very good book which covers many interesting subjects in modern mathematical physics. (Vladimir Mangazeev, The Australian Mathematical Society Gazette, Vol. 33 (4), 2006) This is an extensive volume devoted to the integrability of nonlinear Hamiltonian differential equations. The book is designed as a teaching textbook and aims at a wide readership of mathematicians and physicists, graduate students and professionals. ... The book provides many useful tools and techniques in the field of completely integrable systems. It is a valuable source for graduate students and researchers who like to enter the integrability theory or to learn fascinating aspects of integrable geometry of nonlinear differential equations. (Ma Wen-Xiu, Zentralblatt MATH, Vol. 1083, 2006)

Aus den Rezensionen: ! Um das Noether-Prinzip prazise zu formulieren, muss man einen begrifflichen Rahmen wahlen ! Das vorliegende Buch benutzt die Poissongeometrie ! als einen solchen Rahmen. ! Das vorliegende Buch ist die erste Darstellung des Themenkomplexes in Buchform. Die Autoren haben es als Lehrbuch mit einem weiten Adressatenkreis konzipiert. Dabei hatten sie die schwierige Aufgabe zu bewaltigen, im richtigen Umfang Hintergrundinformationen anzubieten, ohne sich in zusammenhangslosen Einfuhrungen in die relevanten mathematischen Gebiete zu verlieren. Ich denke, dies ist ihnen sehr gut gelungen ! (J. Hilgert, in: Jahresbericht der Deutschen Mathematiker-Vereinigung, 2007, Vol. 107, Issue 1, S. 4-6)

From the reviews of the first edition: The aim of this book is to explain 'how algebraic geometry, Lie theory and Painleve analysis can be used to explicitly solve integrable differential equations'. ... One of the main advantages of this book is that the authors ... succeeded to present the material in a self-contained manner with numerous examples. As a result it can be also used as a reference book for many subjects in mathematics. In summary ... a very good book which covers many interesting subjects in modern mathematical physics. (Vladimir Mangazeev, The Australian Mathematical Society Gazette, Vol. 33 (4), 2006) This is an extensive volume devoted to the integrability of nonlinear Hamiltonian differential equations. The book is designed as a teaching textbook and aims at a wide readership of mathematicians and physicists, graduate students and professionals. ... The book provides many useful tools and techniques in the field of completely integrable systems. It is a valuable source for graduate students and researchers who like to enter the integrability theory or to learn fascinating aspects of integrable geometry of nonlinear differential equations. (Ma Wen-Xiu, Zentralblatt MATH, Vol. 1083, 2006)

From the reviews of the first edition: The aim of this book is to explain 'how algebraic geometry, Lie theory and Painleve analysis can be used to explicitly solve integrable differential equations'. ! One of the main advantages of this book is that the authors ! succeeded to present the material in a self-contained manner with numerous examples. As a result it can be also used as a reference book for many subjects in mathematics. In summary ! a very good book which covers many interesting subjects in modern mathematical physics. (Vladimir Mangazeev, The Australian Mathematical Society Gazette, Vol. 33 (4), 2006) This is an extensive volume devoted to the integrability of nonlinear Hamiltonian differential equations. The book is designed as a teaching textbook and aims at a wide readership of mathematicians and physicists, graduate students and professionals. ! The book provides many useful tools and techniques in the field of completely integrable systems. It is a valuable source for graduate students and researchers who like to enter the integrability theory or to learn fascinating aspects of integrable geometry of nonlinear differential equations. (Ma Wen-Xiu, Zentralblatt MATH, Vol. 1083, 2006)

Author Information

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available