Nonlinear Dynamical Systems Of Mathematical Physics: Spectral And Symplectic Integrability Analysis
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A01=Anatoliy Karl Prykarpatsky
A01=Denis Blackmore
A01=Valeriy Hr Samoylenko
Author_Anatoliy Karl Prykarpatsky
Author_Denis Blackmore
Author_Valeriy Hr Samoylenko
Category=PBWR
Category=PHU
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Integrability Analysis
Integrable Hamiltonian Dynamical Systems
Lax Integrability
Mathematical Physics
Quantum Dynamics
Spectral and Symplectic Methods
Product details
- ISBN 9789814327152
- Publication Date: 08 Mar 2011
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This distinctive volume presents a clear, rigorous grounding in modern nonlinear integrable dynamics theory and applications in mathematical physics, and an introduction to timely leading-edge developments in the field — including some innovations by the authors themselves — that have not appeared in any other book.The exposition begins with an introduction to modern integrable dynamical systems theory, treating such topics as Liouville-Arnold and Mischenko-Fomenko integrability. This sets the stage for such topics as new formulations of the gradient-holonomic algorithm for Lax integrability, novel treatments of classical integration by quadratures, Lie-algebraic characterizations of integrability, and recent results on tensor Poisson structures. Of particular note is the development via spectral reduction of a generalized de Rham-Hodge theory, related to Delsarte-Lions operators, leading to new Chern type classes useful for integrability analysis. Also included are elements of quantum mathematics along with applications to Whitham systems, gauge theories, hadronic string models, and a supplement on fundamental differential-geometric concepts making this volume essentially self-contained.This book is ideal as a reference and guide to new directions in research for advanced students and researchers interested in the modern theory and applications of integrable (especially infinite-dimensional) dynamical systems.
