Algebraic Aspects of Integrable Systems

Algebraic Aspects of Integrable Systems : In Memory of Irene Dorfman

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A collection of articles in memory of Irene Dorfman and her research in mathematical physics. Among the topics covered are: the Hamiltonian and bi-Hamiltonian nature of continuous and discrete integrable equations; the t-function construction; the r-matrix formulation of integrable systems; pseudo-differential operators and modular forms; master symmetries and the Bocher theorem; asymptotic integrability; the integrability of the equations of associativity; invariance under Laplace-darboux transformations; trace formulae of the Dirac and Schrodinger periodic operators; and certain canonical 1-forms.
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Product details

  • Hardback | 350 pages
  • 165.1 x 247.65 x 25.4mm | 676g
  • Secaucus, United States
  • English
  • 1997 ed.
  • X, 350 p.
  • 0817638350
  • 9780817638351

Table of contents

Complex Billiard Hamiltonian Systems and Nonlinear Waves.- Automorphic Pseudodifferential Operators.- On ?-Functions of Zakharov-Shabat and Other Matrix Hierarchies of Integrable Equations.- On the Hamiltonian Representation of the Associativity Equations.- A Plethora of Integrable Bi-Hamiltonian Equations.- Hamiltonian Structures in Stationary Manifold Coordinates.- Compatibility in Abstract Algebraic Structures.- A Theorem of Bochner, Revisited.- Obstacles to Asymptotic Integrability.- Infinitely-Precise Space-Time Discretizations of the Equation ut + uux = 0.- Trace Formulas and the Canonical 1-Form.- On Some "Schwarzian" Equations and their Discrete Analogues.- Poisson Brackets for Integrable Lattice Systems.- On the r-Matrix Structure of the Neumann Systems and its Discretizations.- Multiscale Expansions, Symmetries and the Nonlinear Schroedinger Hierarchy.- On a Laplace Sequence of Nonlinear Integrable Ernst-Type Equations.- Classical and Quantum Nonultralocal Systems on the Lattice.
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