Mathematical Surveys and Monographs 2000; 600 pp; hardcover Volume: 78 ISBN10: 0821814001 ISBN13: 9780821814000 List Price: US$126 Member Price: US$100.80 Order Code: SURV/78
 This book develops a theory that can be viewed as a noncommutative counterpart of the following topics: dynamical systems in general and integrable systems in particular; Hamiltonian formalism; variational calculus, both in continuous space and discrete. The text is selfcontained and includes a large number of exercises. Many different specific models are analyzed extensively and motivations for the new notions are provided. Readership Graduate students, research mathematicians, and physicists interested in global analysis and analysis on manifolds. Reviews "This remarkable book ... is written so as to be completely selfcontained with most arguments presented in great detail ... a remarkable account of a substantial body of work ... likely to remain a significant work of reference as the field continues to develop."  Mathematical Reviews Table of Contents Continuous spacetime  The KP hierarchy
 The mKP hierarchy
 Between KP and mKP
 Noncommutative Lagrangian formalism
 Noncommutative Hamiltonian informalism
 mKP = m + KP
 The quasirelativistic KP hierarchy
 The second construction of integrals of the KP hierarchy
Discrete spacecontinuous time  KP, then mKP
 The noncommutative differentialdifference calculus
 The noncommutative Hamiltonian formalism over differentialdifference
 Hamiltonian formalism for discrete integrable systems of KP and mKP types
 The Gibbons forms
 The hydrodynamical Ansatz
 Relativistic Toda lattice and related systems
Discrete spacetime  The idea of Lax representations and its discretetime analog
 Systems of the KP type
 Systems of mKP type
 The Toda lattice, the relativistic Toda lattice, and related systems
Appendices  Complexification of Hamiltonian systems
 Asymptotic expansions of Hamiltonian systems
 Variational calculus over noncommutative rings
 Hamiltonian correspondencies
 Covariant aspects of the Hamiltonian formalism
 Noncommutative solitons
 The noncommutative KP equation
 A list of scalar equations
 Open problems and conjectures
 Notes and comments
 Bibliography
 Index/notations
