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  1. On the solution of evolution p-Laplace equation with memory term and unknown boundary Dirichlet condition

    In the present paper, we are interested in investigating a classe of nonlinear parabolic integro-differential equation with unknown flux on the part...

    R. Khalfallaoui, A. Chaoui, M. Djaghout in Journal of Elliptic and Parabolic Equations
    Article 14 July 2024
  2. 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....
    Chapter
  3. Index

    Abstract not available
    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...
    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...
    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...
    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,...
    Chapter
  13. A. Proof of Thm. 4.34

    Abstract not available
    Chapter
  14. References

    Abstract not available
    Chapter
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