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  1. Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method

    We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e....
    Micheline Musette in Direct and Inverse Methods in Nonlinear Evolution Equations
    Chapter

  2. Index

    Abstract not available
    Frédéric Cao in Geometric Curve Evolution and Image Processing
    Chapter

  4. Symmetries of Discrete Systems

    In this series of lectures, we review the application of Lie point symmetries, and their generalizations, to the study of difference equations. The...
    Pavel Winternitz in Discrete Integrable Systems
    Chapter

  5. Discrete Painlevé Equations: A Review

    We present a review of what is current knowledge about discrete Painlevé equations. We start with a historical introduction which explains how the...
    B. Grammaticos, A. Ramani in Discrete Integrable Systems
    Chapter

  6. Bilinear Formalism in Soliton Theory

    A brief survey of the bilinear formalism discovered by Hirota is given. First, the procedure to obtain soliton solutions of nonlinear evolution...
    J. Satsuma in Integrability of Nonlinear Systems
    Chapter

  7. Sato Theory and Transformation Groups. A Unified Approach to Integrable Systems

    More than 20 years ago, it was discovered that the solutions of the Kadomtsev-Petviashvili (KP) hierarchy constitute an infinite-dimensional...
    Ralph Willox, Junkichi Satsuma in Discrete Integrable Systems
    Chapter

  8. Ultradiscrete Systems (Cellular Automata)

    Ultradiscretization is a limiting procedure which allows one to obtain a cellular automaton (CA) from continuous equations. Using this method, we can...
    Tetsuji Tokihiro in Discrete Integrable Systems
    Chapter

  9. Time in Science: Reversibility vs. Irreversibility

    To discuss properly the question of irreversibility one needs to make a careful distinction between reversibility of the equations of motion and the...
    Yves Pomeau in Discrete Integrable Systems
    Chapter

  10. Nonlinear Waves, Solitons, and IST

    These lectures are written for a wide audience with diverse backgrounds. The subject is approached from a general perspective and overly detailed...
    M.J. Ablowitz in Integrability of Nonlinear Systems
    Chapter

  11. Integrability – and How to Detect It

    We present a physicist’s approach to integrability and its detection. Starting from specific examples we present a working definition of what is...
    B. Grammaticos, A. Ramani in Integrability of Nonlinear Systems
    Chapter

  12. Introduction

    Nonlinear systems model all but the simplest physical phenomena. In the classical theory, the tools of Poisson geometry appear in an essential way,...
    The Editors in Integrability of Nonlinear Systems
    Chapter

  13. A. Proof of Thm. 4.34

    Abstract not available
    Frédéric Cao in Geometric Curve Evolution and Image Processing
    Chapter

  18. Basic Principles of Classical Mechanics

    To describe the motion of mechanical systems one uses a variety of mathematical models which are based on different principles - laws of motion. In...
    V. I. Arnold, V. V. Kozlov, A. I. Neishtadt in Mathematical Aspects of Classical and Celestial Mechanics
    Chapter

  19. References

    Abstract not available
    Frédéric Cao in Geometric Curve Evolution and Image Processing
    Chapter
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