Lie Algebraic Methods in Integrable Systems

Amit K. Roy-Chowdhury

ISBN 10: 1584880376 / ISBN 13: 9781584880370

Verlag: Chapman And Hall/CRC, 1999

Beschreibung

nach der Bestellung gedruckt Neuware - Printed after ordering - In recent decades, the study of nonlinear integrable systems has grown into a full-fledged research topic. The ideas associated with Lie algebra and groups can form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author presents the techniques for using Lie algebraic concepts to explore nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as a tool. The text summarizes the use of these methods in various fields of theoretical research and serves mathematicians and theoretical physicists working in nonlinear integrable systems, dynamical systems, and chaos.

Bestandsnummer des Verkäufers 9781584880370

Bibliografische Details

• Titel: Lie Algebraic Methods in Integrable Systems
• Verlag: Chapman And Hall/CRC
• Erscheinungsjahr: 1999
• Sprache: Englisch
• ISBN-10: 1584880376
• ISBN-13: 9781584880370
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 234B x 156 H x 20 T Millimeter Breite: 234 mm, Höhe: 156 mm, Tiefe: 20 mm
• Gewicht: 559 Gramm

Über diesen Titel

Inhaltsangabe

Over the last thirty years, the subject of nonlinear integrable systems has grown into a full-fledged research topic. In the last decade, Lie algebraic methods have grown in importance to various fields of theoretical research and worked to establish close relations between apparently unrelated systems. The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool. The book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation. It then offers a detailed discussion of prolongation structure and its representation theory, the orbit approach-for both finite and infinite dimension Lie algebra. The author also presents the modern approach to symmetries of integrable systems, including important new ideas in symmetry analysis, such as gauge transformations, and the "soldering" approach. He then moves to Hamiltonian structure, where he presents the Drinfeld-Sokolov approach, the Lie algebraic approach, Kupershmidt's approach, Hamiltonian reductions and the Gelfand Dikii formula. He concludes his treatment of Lie algebraic methods with a discussion of the classical r-matrix, its use, and its relations to double Lie algebra and the KP equation.

Über die Autorin bzw. den Autor

Amit K. Roy-Chowdhury (University of California, Riverside, USA) (Author)