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  1. Introduction

    In classical mechanics a well defined concept of integrability exists which is related to the Hamiltonian description of mechanics. If the phase...
    Chapter
  2. Exact solutions of nonlinear partial differential equations by singularity analysis

    Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with...
    Chapter
  3. Hirota bilinear method for nonlinear evolution equations

    The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples...
    Chapter
  4. References

    Abstract not available
    Chapter
  5. Discrete Lagrangian Models

    These lectures are devoted to discrete integrable Lagrangian models. A large collection of integrable models is presented in the Lagrangian fashion,...
    Chapter
  6. Discrete Differential Geometry. Integrability as Consistency

    We discuss a new geometric approach to discrete integrability coming from discrete differential geometry. A d–dimensional equation is called...
    Alexander I. Bobenko in Discrete Integrable Systems
    Chapter
  7. Special Solutions for Discrete Painlevé Equations

    We construct special solutions for the discrete Painlevé equations. We start with a review of the corresponding solutions in the case of the...
    K.M. Tamizhmani, T. Tamizhmani, ... A. Ramani in Discrete Integrable Systems
    Chapter
  8. Special Solutions of Discrete Integrable Systems

    Hierarchies of discrete soliton equations are constructed in bilinear form as a consequence of the algebraic identities satisfied by determinants and...
    Chapter
  9. Topological Quantum Field Theory and Algebraic Structures*

    These notes are from lectures given at the Quantum field theory and noncommutative geometry workshop at Tohoku University in Sendai, Japan from...
    Chapter
  10. On Gauge Transformations of Poisson Structures

    We discuss various questions in Poisson geometry centered around the notion of gauge transformations associated with 2-forms. The topics in this note...
    Chapter
  11. Gauge Theories on Noncommutative Spacetime Treated by the Seiberg-Witten Method*

    The idea of noncommutative coordinates (NCC) is almost as old as quantum field theory (QFT) itself. It was W.Heisenberg who proposed NCC in 1930 in a...
    Chapter
  12. Introduction to String Compactification

    We present an elementary introduction to compactifications with unbroken supersymmetry. After explaining how this requirement leads to internal...
    Chapter
  13. Noncommutative Spheres and Instantons

    We report on some recent work on deformation of spaces, notably deformation of spheres, describing two classes of examples.
    Chapter
  14. Classification of All Quadratic Star Products on a Plane* **

    In this paper we classify all quadratic star products on a plane by using Hochschild cohomology and Poisson cohomology.
    Chapter
  15. Morita Equivalence, Picard Groupoids and Noncommutative Field Theories

    In this article we review recent developments on Morita equivalence of star products and their Picard groups. We point out the relations between...
    Chapter
  16. Universal Deformation Formulae for Three-Dimensional Solvable Lie Groups

    We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of every...
    P. Bieliavsky, P. Bonneau, Y. Maeda in Quantum Field Theory and Noncommutative Geometry
    Chapter
  17. Knot Invariants and Configuration Space Integrals

    After a short presentation of the theory of Vassiliev knot invariants, we shall introduce a universal finite type invariant for knots in the ambient...
    Chapter
  18. 3 Complexity, Uncertainty and Surprise: An Integrated View

    The purpose of this paper is to tie together some of the major themes that emerged at the conference and in the presentations in this volume. As...
    Dean J. Driebe, Reuben R. McDaniel in Uncertainty and Surprise in Complex Systems
    Chapter
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