Classical and Quantum Nonlinear Integrable Systems

"This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems … different chapters are written by different authors … all authors put an emphasis on describing the general ideology rather than on technical details.A reader interested in classical methods of solitons, such as the methods of solving the KdV equation can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5. Thus the book should appeal and be useful to a wide range of theoretical physicists.In summary, this reviewer believes that this book is an excellent introduction to a wide range of methods and applications of the theory of integrable systems. It should be useful both to researchers working in some aspect of the field of integrable systems, who would like to broaden their knowledge of the subject, as well as to those who would like to enter the subject including Ph.D. students."-Tomasz Brzezinski, Department of Mathematics, University of Wales, Swanseais a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems … different chapters are written by different authors … all authors put an emphasis on describing the general ideology rather than on technical details.A reader interested in classical methods of solitons, such as the methods of solving the KdV equation can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5. Thus the book should appeal and be useful to a wide range of theoretical physicists.In summary, this reviewer believes that this book is an excellent introduction to a wide range of methods and applications of the theory of integrable systems. It should be useful both to researchers working in some aspect of the field of integrable systems, who would like to broaden their knowledge of the subject, as well as to those who would like to enter the subject including Ph.D. students."-Tomasz Brzezinski, Department of Mathematics, University of Wales, Swansea

• Preface (A Kundu) A Journey Through the KdV Equation (M Lakshmanan) The Painleve methods (R Conte and M Musette) Discrete Integrability (K M Tamizhmani, A Ramani, B Grammaticos and T Tamizhmani) The D-BAR Method: A Tool for Solving Two-Dimensional Integrable Evolution PDEs (A S Fokas) Introduction to Solvable Lattice Models in Statistical and Mathematical Physics (T Deguchi)II. QUANTUM SYSTEMS Unifying Approaches in Integrable Systems: Quantum and Statistical, Ultralocal and Nonultralocal (A Kundu) The Physical Basis of Integrable Spin Models (I Bose) Exact Solvability in Contemporary Physics (A Foerster, J Links and H-Q Zhou) The Thermodynamics of the spin-1/2 XXX Chain: Free Energy and Low-temperature Singularities of Correlation Lengths (A Klümper and C Scheeren) Reaction-Diffusion Processes and Their Connection with Integrable Quantum Spin Chains (M Henkel)