Integrable systems

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Programme theme

The modern theory of integrability was created and developed over the last thirty years by a number of international research groups. Several approaches to integrable equations have been elaborated, which look quite different but focus on solutions of the same range of problems. One of the aims of this programme is to bring together key scientists with various background and expertise in order to elaborate a coherent view on the problem and to attempt to develop a synthetic theory which would reconcile the different approaches. This will be the first meeting on such a scale and we expect that mutual understanding of different approaches will cause a breakthrough in the whole theory of integrable equations and significantly extend its applications.

The following methods for studying integrability will be discussed

The Painlevé approach
The perturbation theory approach
Asymtotic expansions methods
The symmetry approach

In addition the "dressing method", and its many variations, will be looked at as a technique for constructing and solving integrable systems. The topic of Quantum Integrability will also be addressed. Links between the classical dressing method and various approaches to quantum systems will be studied. A fundamental issue is a classification of algebraic and differential reductions "inside" the integrable systems which have been constructed.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme
Projectively equivalent Riemannian metrics on the torus Authors: Vladimir Matveev Download PDF	2001	ITS
Multidimensional Schrödinger equations with Abelian potentials Authors: Chris Eilbeck, Victor Enolskii, ET Al, VM Buchstaber Download PDF	2001	ITS
Reflectionless analytic difference operators III. Hilbert space aspects Authors: SNM Ruijsenaars Download PDF	2001	ITS
On the initial-boundary value problem for soliton equations Authors: Sergei Manakov, Paolo Maria Santini, Antonio Degasperis Download PDF	2001	ITS
Lie point symmetries and commuting flows for equations on lattices Authors: Pavel Winternitz, D Levi Download PDF	2001	ITS
A new integrable equation with peakon solutions Authors: DD Holm, Andrew Hone, Antonio Degasperis Download PDF	2001	ITS
Nonlinear dynamics on the plane and integrable hierarchies of infinitesimal deformations Authors: L Martinez Alonso, Boris Konopelchenko Download PDF	2001	ITS
Reductions and hodograph solutions of dispersionless KP hierarchy Authors: L Martinez Alonso, Elena Medina, Manuel Manas Download PDF	2001	ITS
Tau-functions and special solutions in a coupled Painlevé system Authors: Andrew Hone Download PDF	2001	ITS

Workshops

ITSW01

Seminars

Friday 3rd August 2001
14:00 to 15:00	Jan Sanders Vrije Universiteit Amsterdam On the application of number theory to integrable systems	Discussion Room

Monday 6th August 2001
14:00 to 15:00	Vladimir Zakharov Spaces of diagonal curvature and n-wave systems	Room 1

Wednesday 8th August 2001
14:00 to 15:00	Transient vortex events and the initial value problem for turbulence	Room 1

Wednesday 29th August 2001
15:00 to 16:00	Yuji Kodama Ohio State University Shallow water waves and normal forms	Room 2

Friday 31st August 2001
15:00 to 16:00	Boris Konopelchenko Nonlinear dynamics on the plane, dispersionless integrable hierarchies and the quasi-classical D-BAR dressing method	Room 2

Wednesday 19th September 2001
15:00 to 16:00	Integrable difference geometry vs integrable differential geometry: The discrete ``Lame system"	Room 1

Monday 24th September 2001
15:00 to 16:00	Luis Martinez-Alonso The quasi-classical D-Bar method for the dispersionless KP hierarchy	Room 2

Monday 1st October 2001
15:00 to 16:00	Reflectionless self-adjoint difference operators: from discrete to analytic	Room 1

Wednesday 3rd October 2001
15:00 to 16:00	Lie symmetries and Hirota maps	Room 1

Monday 8th October 2001
15:00 to 16:00	Hermann Flaschka A search for action-angle co-ordinates	Room 1

Wednesday 10th October 2001
15:00 to 16:00	On a class of many-body problems in the plane (including integrable and nonintegrable cases) which possess a lot of periodic solutions	Room 1

Monday 15th October 2001
15:00 to 16:00	Whitham equations, Bergman kernel and logarithmic potential theory	Room 1

Wednesday 17th October 2001
11:00 to 12:00	Victor Enolskii Periods of hyperelliptic integrals expressed in terms of $\theta$- constants by means of Thomae formulae	Room 1

Thursday 18th October 2001
11:00 to 12:00	On a class of many-body problems in the plane (including integrable and nonintegrable cases) which possess a lot of periodic solutions	Room 2

Monday 22nd October 2001
15:00 to 16:00	Vassilios Rothos University of Leeds/University of Loughborough Homoclinic orbits for a modified KdV equation	Room 1

Wednesday 24th October 2001
11:00 to 12:00	John Gibbons Imperial College London Solution methods for Benney's equations	Room 1

Monday 29th October 2001
15:00 to 16:00	Differential-difference KP equation: solutions through Sato approach	Room 2

Wednesday 31st October 2001
11:00 to 12:00	Serguei Tsarev Explicit integration of classical series of exponential systems using the approach of Darboux-Moutard-Goursat	Room 1

Monday 5th November 2001
15:00 to 16:00	Andrei Kapaev Quasi-linear Stokes phenomenon for the second Painlev\'e transcendent	Room 1

Wednesday 7th November 2001
11:00 to 12:00	Compatible Lie brackets and integrable $\sigma$-models	Room 1

Monday 12th November 2001
15:00 to 16:00	Andrei Pogrebkov Steklov Mathematical Institute, Russian Academy of Sciences Inverse scattering transform for the perturbed 1-soliton potential of the nonstationary Schroedinger and heat equations	Room 1

Wednesday 14th November 2001
11:00 to 12:00	Victor Novokshenov Pereslavl-Zalessky of the Russian Academy of Sciences Analytic representation of DM-solitons in the NLS equation	Room 1
14:00 to 15:30	Ecology workshop	Discussion Room

Monday 19th November 2001
15:00 to 16:00	Yura Brezhnev Uniformisation of algebraic curves: on the Burnside curve	Room 2

Wednesday 21st November 2001
11:00 to 12:00	Algebro-geometric solutions of the Camassa-Holm hierarchy	Room 1

Monday 26th November 2001
10:00 to 11:00	Algebraic properties of Hirota derivatives	Room 1
11:30 to 12:30	Atsushi Matsuo Vertex operator algebra and the moonshine module	Room 1
14:30 to 15:30	Symmetric powers of algebraic varieties	Room 1
15:45 to 16:45	Periods of hyperelliptic integrals and Thomae formulae	Room 1

Tuesday 27th November 2001
10:00 to 11:00	Bloch varieties for some two-dimensional Lame operators	Room 1
11:30 to 12:30	Mikhail Feigin Loughborough University Quasi-invariants of Coxeter groups and m-harmonic polynomials	Room 1
14:30 to 15:30	Integrable ODE's on free associative algebras	Room 1
16:00 to 17:00	Atsushi Matsuo Vertex opterator alegbra and the moonshine module - part II	Room 1

Wednesday 28th November 2001
10:00 to 11:00	Noncommutative and quantum spheres: an overview	Room 1
11:30 to 12:30	Yuri Berest Cornell University Geometry without points	Room 1
14:30 to 15:30	Pavel Etingof Acclarogen Limited Representations of the rational Cherednik algebra and alebraic integrability of Calogero-Moser systems I	Room 1
16:00 to 17:00	Sergei Barannikov Quantum periods and integrable hierarchies I	Room 1

Thursday 29th November 2001
10:00 to 11:00	Sergei Barannikov Quantum periods and integrable hierarchies II	Room 1
11:30 to 12:30	Pavel Etingof Acclarogen Limited Representations of the rational Cherednik algebra and algebraic integrability of Calogero-Moser systems II	Room 1
14:30 to 15:30	Atsushi Matsuo Vertex operator algebra and the moonshine module - part III	Room 1
16:00 to 17:00	TBA	Room 1

Wednesday 5th December 2001
15:00 to 17:00	Martin Kruskal Surreal numbers	Discussion Room

Monday 10th December 2001
15:00 to 16:30	John Elgin Imperial College London Finite gap solutions of the vector nonlinear Schroedinger equation	Room 2

Wednesday 12th December 2001
11:00 to 12:30	Manuel Manas Universidad Complutense de Madrid Reductions and hodograph solutions of the dispersionless KP hierarchy	Room 2

Thursday 13th December 2001
14:00 to 15:00	Serguei Tsarev The Monge problem: does it really help to park your car?	Room 2
15:00 to 15:30	Vladimir Matveev Université de Bourgogne Wronskian addition theorem for sine functions and isospectral deformations of Darboux-Poeshl-Teller potentials	Room 2

Wednesday 19th December 2001
11:00 to 12:30	Perturbative symmetry approach and integrability conditions for non- local equations	Room 1

Organisers

Chris Eilbeck Heriot-Watt University
Alexander Mikhailov University of Leeds
Paolo Santini
Vladimir Zakharov

Speakers

Sergei Barannikov
Yuri Berest Cornell University
Yura Brezhnev
John Elgin Imperial College London
Victor Enolskii
Pavel Etingof Acclarogen Limited
Mikhail Feigin Aalborg Universitet
Hermann Flaschka
John Gibbons Imperial College London
Andrei Kapaev
Yuji Kodama Ohio State University
Boris Konopelchenko
Martin Kruskal
Manuel Manas Universidad Complutense de Madrid
Luis Martinez-Alonso
Atsushi Matsuo
Vladimir Matveev Université de Bourgogne
Victor Novokshenov Pereslavl-Zalessky of the Russian Academy of Sciences
Andrei Pogrebkov Steklov Mathematical Institute, Russian Academy of Sciences
Vassilios Rothos University of Leeds/University of Loughborough
Jan Sanders Vrije Universiteit Amsterdam
Serguei Tsarev
Vladimir Zakharov

Show All

Programme theme

Preprints

Projectively equivalent Riemannian metrics on the torus

Multidimensional Schrödinger equations with Abelian potentials

Reflectionless analytic difference operators III. Hilbert space aspects

On the initial-boundary value problem for soliton equations

Lie point symmetries and commuting flows for equations on lattices

A new integrable equation with peakon solutions

Nonlinear dynamics on the plane and integrable hierarchies of infinitesimal deformations

Reductions and hodograph solutions of dispersionless KP hierarchy

Tau-functions and special solutions in a coupled Painlevé system

Workshops

NEEDS - nonlinear evolution equations and dynamical systems XVth meeting

What is integrability?

Discrete systems and integrability

Geometrical aspects of integrability

Computer algebra in applications to the problems of integrability

Algebraic aspects of integrability

Classical and quantum integrable systems

Boundary value problems

Seminars

Organisers

Speakers

Supported By

Integrable systems

Programme theme

Preprints

Projectively equivalent Riemannian metrics on the torus

Multidimensional Schrödinger equations with Abelian potentials

Reflectionless analytic difference operators III. Hilbert space aspects

On the initial-boundary value problem for soliton equations

Lie point symmetries and commuting flows for equations on lattices

A new integrable equation with peakon solutions

Nonlinear dynamics on the plane and integrable hierarchies of infinitesimal deformations

Reductions and hodograph solutions of dispersionless KP hierarchy

Tau-functions and special solutions in a coupled Painlevé system

Workshops

Seminars

Organisers

Speakers

Supported By

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