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  1. 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...
    Y. Ohta in Discrete Integrable Systems
    Chapter

  2. Discrete Lagrangian Models

    These lectures are devoted to discrete integrable Lagrangian models. A large collection of integrable models is presented in the Lagrangian fashion,...
    Yu.B. Suris in Discrete Integrable Systems
    Chapter

  3. Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: A Review and Extensions of Tests for the Painlevé Property

    The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity...
    Martin D. Kruskal, Nalini Joshi, Rod Halburd in Integrability of Nonlinear Systems
    Chapter

  4. 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

  5. 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...
    Junkichi Satsuma in Direct and Inverse Methods in Nonlinear Evolution Equations
    Chapter

  6. 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...
    Robert Conte in Direct and Inverse Methods in Nonlinear Evolution Equations
    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

  11. Lie Bialgebras, Poisson Lie Groups, and Dressing Transformations

    In this course, we present an elementary introduction, including the proofs of the main theorems, to the theory of Lie bialgebras and Poisson Lie...
    Yvette Kosmann-Schwarzbach in Integrability of Nonlinear Systems
    Chapter

  12. Introduction to the Hirota Bilinear Method

    We give an elementary introduction to Hirota’s direct method of constructing multi-soliton solutions to integrable nonlinear evolution equations. We...
    J. Hietarinta in Integrability of Nonlinear Systems
    Chapter

  13. Eight Lectures on Integrable Systems

    These lectures provide an introduction to the theory of integrable systems from the point of view of Poisson manifolds. In classical mechanics, an...
    F. Magri, P. Casati, ... M. Pedroni in Integrability of Nonlinear Systems
    Chapter

  14. Three Lessons on the Painlevé Property and the Painlevé Equations

    While this school focuses on discrete integrable systems we feel it necessary, if only for reasons of comparison, to go back to fundamentals and...
    M.D. Kruskal, B. Grammaticos, T. Tamizhmani in Discrete Integrable Systems
    Chapter

  15. Quantum and Classical Integrable Systems

    The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the...
    M.A. Semenov-Tian-Shansky in Integrability of Nonlinear Systems
    Chapter

  16. Lie groups, singularities and solutions of nonlinear partial differential equations

    It is shown how Lie group and Lie algebra theory can be used to solve partial differential equations. A method for calculating the symmetry group of...
    Pavel Winternitz in Direct and Inverse Methods in Nonlinear Evolution Equations
    Chapter

  17. The method of Poisson pairs in the theory of nonlinear PDEs

    The aim of these lectures is to show that the methods of classical Hamiltonian mechanics can be profitably used to solve certain classes of nonlinear...
    Franco Magri, Gregorio Falqui, Marco Pedroni in Direct and Inverse Methods in Nonlinear Evolution Equations
    Chapter
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