(This page is under construction and many items are still missing)
The Red Book
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
- F. Nijhoff, J Atkinson and J. Hietarinta: Soliton solutions for ABS lattice equations: I. Cauchy matrix approach, J. Phys. A: Math. Theor. 42 404005 (34 pages) (2009).
- J. Hietarinta and Da-Jun Zhang: Soliton solutions for ABS lattice equations: II. Casoratians and bilinearization, J. Phys. A: Math. Theor. 42 404006 (30 pages) (2009).
- J Atkinson, J. Hietarinta and F Nijhoff: Soliton solutions for Q3, J. Phys. A: Math. Theor. 41
142001 (11 pages) (2008). - J Atkinson, J. Hietarinta and F Nijhoff: Seed and soliton solutions for Adler’s lattice equation, J. Phys. A: Math. Theor. 40 F1-F8 (2007).
Searches
- J. Hietarinta and C. Viallet: Searching for integrable lattice maps using factorization, J. Phys. A: Math. Theor. 40 12629-12643 (2007).
- J. Hietarinta: Searching for CAC-maps, J. Nonlinear Math. Phys. 12 Suppl. 2, 223-230 (2005).
- J. Hietarinta: A new two-dimensional lattice model that is’consistent around the cube’, J. Phys. A: Math.
Gen. 37, L67-L73 (2004)
Singularity confinement and algebraic entropy
- J. Hietarinta and C. Viallet: Discrete Painlevé I and singularity confinement in projective space, Chaos, Solitons and Fractals 11, 29-32 (2000).
- J. Hietarinta and C. Viallet: Singularity confinement and chaos in discrete systems, Phys. Rev. Lett. 81, 325-328 (1998).
- J. Hietarinta: Regularity of Difference Equations, in “Difference Equations and Discrete Dynamical Systems” eds. L. Allen, B. Aulbach, S. Elaydi and R. Sacker, (World Scientific, 2005) pp. 233-245.
- J. Hietarinta: Integrability tests for difference equations, Nonlinear Analysis 47, 4641-4650 (2001).
- J. Hietarinta and C. Viallet: Singularity Confinement and Degree Growth, CRM Proceedings and Lecture Notes 25, 209-216 (2000).
Discrete Painlevé equations
- A. Ramani, B. Grammaticos and J. Hietarinta: Discrete versions of the Painlevé Equation, Phys. Rev. Lett. 67, 1829-1831 (1991).
- J. Hietarinta and K. Kajiwara: Rational solutions to d-PIV , in “Symmetries and Integrability of Difference Equations”, eds. P. Clarkson and F. Nijhoff, London Mathematical Society Lecture Note Series 255 (Cambridge UP, 1999) pp. 206-216.
- J. Satsuma, K. Kajiwara, B. Grammaticos, J. Hietarinta and A. Ramani: Bilinear discrete Painlevé-II and its particular solutions, J. Phys. A: Math. Gen. 28, 3541-3548 (1995).