Lie Algebraic Methods in Integrable Systems
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.
- 1999 Chapman
Choosing a Book Format
EPUB is the standard publishing format used by many e-book readers including iBooks, Easy Reader, VoiceDream Reader, etc. This is the most popular and widely used format.
DAISY format is used by GoRead, Read2Go and most Kurzweil devices.
Audio (MP3) format is used by audio only devices, such as iPod.
Braille format is used by Braille output devices.
DAISY Audio format works on DAISY compatible players such as Victor Reader Stream.
Accessible Word format can be unzipped and opened in any tool that supports .docx files.