Discrete Integrability

(This page is under construction and many items are still missing)

The Red Book

Discrete Systems and Integrability

Discrete Systems and Integrability by J. Hietarinta, N. Joshi and F Nijhoff.

“This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments.  The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples.  The book contains a thorough list of references.”

Available at amazon.com  amazon.co.uk amazon.de amazon.fr amazon.it  amazon.cn  amazon.in  amazon.jp  and of course at CUP .

Lectures and talks

(links still broken, also more talks to come)

Talk at SIDE IX Bangalore 2014 and in Leeds 2015 on Discrete Boussinesq equations.

Lectures series Definitions and Predictions of Integrability for Difference Equations given at the SMS-Summer School “Symmetries and Integrability of Difference Equations”, Montreal, June 9-21, 2008:

  • Lectures 1 and 2 (singularity confinement and algebraic entropy for maps)
  • Lecture 3 (singularity confinement and algebraic entropy for lattices)
  • Lecture 4 (consistency-around-the-cube)

Soliton solution to Lattice equations

Searches

Singularity confinement and algebraic entropy

Discrete Painlevé equations