Discrete Integrable Systems

Discrete Integrable Systems's image
Created: 2009-03-13 09:28
Institution: Isaac Newton Institute for Mathematical Sciences
Description: The theory of (ordinary and partial) differential equations is well-established and to some extent standardised. By contrast, the theory of difference equations, while more fundamental, has until recently been in its infancy, in spite of a major effort at the beginning of the 20th Century by N"orlund and the school of G.D. Birkhoff to establish the linear theory. Discrete systems can appear in two main guises: in the first case the independent variable is discrete, taking values on a lattice (e.g. finite-difference equations, such as recurrence relations and dynamical mappings), in the second case the independent variable is continuous (e.g. analytic difference equations and even functional equations).

Very recently, however, mainly through advances in the theory of exactly integrable discrete systems and the theory of (linear and nonlinear) special functions, the study of difference equations has undergone a true revolution. For the first time good and interesting examples of nonlinear difference equations admitting exact, albeit highly nontrivial, solutions were found and this has led to the formulation of novel approaches to the classification and treatment of such equations. Thus, an area has developed where several branches of mathematics and physics, that are usually distinct, come together: complex analysis, algebraic geometry, representation theory, Galois theory, spectral analysis and the theory of special functions, graph theory, and difference geometry.

Read more at: www.newton.ac.uk/programmes/DIS/
 

Media items

This collection contains 155 media items.

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Media items

QRT Maps & Elliptic Surfaces

   1,614 views

Johannes Jisse Duistermaat (Universiteit Utrecht)
Monday 18 May 2009, 17:00-18:00

Collection: Rothschild Seminars

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 16 Mar 2011


A completeness study on a class of Lax pairs

   692 views

Hay, M (Kyushu)
Thursday 02 July 2009, 11:30-12:00
Discrete Systems and Special Functions

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 15 Mar 2011


A discrete system from the recurrence coefficients of 2-variable elliptic orthogonal polynomials

   447 views

Spicer, P (KL Leuven)
Tuesday 30 June 2009, 14:00-14:30
Discrete Systems and Special Functions

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 15 Mar 2011


A Galois D-groupoid for q-difference equations

   507 views

Granier, A (Institut de Mathematiques de Toulouse)
Tuesday 09 June 2009, 11:00-12:00

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 24 Jun 2009


A new extended discrete KP hierarchy and its solutions

   539 views

Yao, Y (Tsinghua)
Thursday 02 July 2009, 14:30-15:00
Discrete Systems and Special Functions

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 16 Mar 2011


Abelian Integrals over Complex Curves and Lattice Integrals over Tropical Curves

   719 views

Shinsuke Iwao (Tokyo)
Thursday 02 April 2009, 16:15-17:00
Geometric Aspects of Discrete and Ultra-discrete Integrable Systems

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Thu 10 Mar 2011


Abelian solutions of difference equations

   717 views

Krichever, I (Columbia)
Wednesday 10 June 2009, 14:00-14:50

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 24 Jun 2009


Admissibility of solutions of discrete dynamical systems

   544 views

Halburd, R (UCL)
Thursday 14 May 2009, 16:30-17:30
Algebraic Theory of Difference Equations

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 14 Mar 2011


Algebra and algorithms for the classification of differential invariants

   655 views

Hubert, E (INRIA Sophia Antipolis)
Monday 29 June 2009, 15:30-16:30
Discrete Systems and Special Functions

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 15 Mar 2011


Algebra and geometry of Somos sequences

   725 views

Hone, A (Kent)
Wednesday 04 March 2009, 15:10-16:00

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 7 Mar 2011


An unification of field, lattice and q-deformed soliton systems as integrable evolution equations on regular times...

   526 views

Blazej Szablikowski (Glasgow)
Monday 30 March 2009, 16:15-17:00
Geometric Aspects of Discrete and Ultra-discrete Integrable Systems

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Thu 10 Mar 2011


Analytic solutions to the q-Painlevé equations around the origin

   630 views

Ohyama, Y (Osaka)
Friday 03 July 2009, 14:00-14:30
Discrete Systems and Special Functions

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 16 Mar 2011


Area-perimeter generating functions of lattice walks: q-series and their asymptotics

   536 views

Prellberg, T (QMUL)
Wednesday 01 July 2009, 11:30-12:00
Discrete Systems and Special Functions

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 15 Mar 2011


Arithmetic theory of q-difference equations

   589 views

di Vizio, L (CNRS, IMJ, Paris)
Thursday 14 May 2009, 11:00-12:00
Algebraic Theory of Difference Equations

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 14 Mar 2011


Ax's theorem for additive power series

   656 views

Kowalski, P (Wroclaw)
Thursday 14 May 2009, 14:00-15:00
Algebraic Theory of Difference Equations

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 14 Mar 2011


Bianchi (hyper-)cubes and a geometric unification of the Hirota and Miwa equations

   295 views

Schief, W (University of New South Wales)
Monday 08 July 2013, 11:00-11:30

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 12 Jul 2013


Bilinearization and soliton solutions for the ABS list

   2,378 views

Hietarinta, J (Turku)
Wednesday 11 February 2009, 14:00-14:50

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 7 Mar 2011


Bispectral quantum KZ equations and their solutions

   618 views

Stokman, J (Universiteit van Amsterdam)
Thursday 02 July 2009, 09:00-10:00
Discrete Systems and Special Functions

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 15 Mar 2011


Bletchley Park 1942 - 1945

   1,317 views

Loewe, M
Tuesday 16 June 2009, 17:00-18:00

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 3 Jul 2009


Box-Ball system and Toda equation

   829 views

Tetsuji Tokihiro (Tokyo)
Monday 30 March 2009, 11:30-12:15
Geometric Aspects of Discrete and Ultra-discrete Integrable Systems

Collection: Discrete Integrable Systems

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 1 May 2009


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