Physlca 2D (1981) 545-548 North-Holland Pubhshmg Company

WORKSHOP ON NONLINEAR EVOLUTION EQUATIONS AND DYNAMICAL SYSTEMS THE ORTHODOX ACADEMY OF CRETE, CHANIA, CRETE, JULY 9-23,198O

A SHORT SUMMARY

Francesco CALOGERO Istltuto dl Ftsrca, Umuersltci dl Roma, 00185 Roma, Italy

and

Andonis VERGANELAKIS Nuclear Research Center Demokntos, Aghra Paraskevr Attrkls, Athens, Greece

Received 24 November 1980

1. Introduction

The Workshop took place at the Orthodox Academy near Chama m Crete, a modern budding with local charac- ter, located m a splendid environment by the sea There were 72 participants from 18 countries (see the list of participants below) All participants had all theu meals at the Academy, and a maJority also roomed there, the others bemg accommodated wrthm walkmg distance at the nearby village of Kohmbari. These arrangements, and the caliber of the participants, created a sclentlfically stlmulatmg yet generally relaxing and friendly atmosphere, conducive to much actlvlty and many exchanges In ad&Ion to the talks listed below, a number of informal “nonsemmars” were organized by various groups Some were announced m advance by the core group that convened them, for Instance, one on “vortices (mostly on stationary configurations)“, one on “prolongation structures”, one on “extended classlcal obJects as models of elementary particles”, one on “fac- tortzatlon of operators, Mmra maps, modltied Lax equations and all that”, one on “adding sohtons by Backlund trans- formatlons” Other nonsemmars coaiesced spontaneously around a blackboard or a table and we have no record of them In addltlon to these collective actlvltles, there were Innumerable personal contacts, which perhaps constituted the most useful aspect of the Workshop They were of many kinds Joint actlvlty by research partners who took ad- vantage of the Workshop to meet and work together (at least one paper was completed during the Workshop, Its two coauthors hvmg normally on opposite sides of the Atlantic); the personal encounter of scholars, who had never met before but knew each other through their pubhshed works; and the opportunity for all partlclpants to meet and befriend other researchers with similar interests Mathematics and physics were Indeed talked about almost nonstop for two weeks some people would wake up before dawn, to enJoy an early swim, watch the lovely colours of sea and sky as

mght turns mto day, and do some quiet ttunkmg, writing, talking; whde conversations went on late mto the night Two one-day excursions were orgamzed to the Samaria Gorge (most participants were brave enough to walk 18 km down the gorge), and to the Knossos archeologlcal site Both excursions included an open au dinner on the way back There was also a collective visit to Chama one evening, culmmatmg m the attendance of an open air rally-concert- recital by Mlki Theodorakls (in the stadium, with many thousands other people, Theodorakls IS himself from Chama)

The mam source of financial support for the Workshop was provided by the participants themselves (at a basic all inclusive rate of $450 per participant, $375 per accompany- mg adult) There were about IO guests, mainly from coun- tries with nonconvertible currencies; and reduced rates for the participants from the host country A grant of IO5 drachmas (appr $2 500) from the Motor 011 (Hellas) Com- pany IS gratefully acknowledged, m ad&Ion to some sup- port from the sponsoring mstltutions the Nuclear Research Center Demokritos m Athens and the Umversltles of Crete, of Lecce and of Rome

This Workshop was lmmedlately preceded by another one, on “Gauge Theories and their Phenomenologlcal Im- phcatlons” (at the Orthodox Academy, June 29-July 9) Both Workshops were affected by an Olimpic Alrways strike, July 7-10, the begmnmg of the sclenttfic program of this Workshop had to be postponed by half a day and somewhat rearranged Proceedings of both Workshops (m- eluding Abstracts of all contnbutlons) have been Issued as pubhcatlons from the N R C Demokrltos

As organizers of this Workshop, we were gratified by the collaborative and friendly mood that constituted the resonant mode to which the participants appeared to be locked throughout this venture This was certainly the most Important element to make the Workshop scientIfically suc- cessful and generally enjoyable

0167-2789/81/OOOO4MO /$02.50 @ North-Holland Publishing Company

546 Francesco Calogero and Andonls Verganelaklsl Workshop on dynamical systems

2. Scheduled program

A prehnunary tentative program was distributed to the particrpants as they arrived A Scientific Steermg Committee (Ablowltz, Calogero, Percival, Perelomov, Verganelakrs) had been set up to prepare the final program, on the basis of the feedback from all participants Actually, no changes were requested, so that the program could be finalized easily and quickly (as soon as the transient due to the airways strike was overcome) This program was distributed by the third day, and was subsequently followed throughout the Workshop, up to rnmlmal modlficatlons This indicates the accommodatmg and cooperative spirit that prevailed during the entire meeting, It was Instrumental to provide a firm organizational backbone around which all other informal actlvitles found then appropriate place The final version of the scheduled program, as It was actually Implemented, IS reported below (the names m boldface letters are those of the participants who presented the contribution)

Wednesday, July 9 Arrival of participants

Thursday, July 10 17 00 A. VERGANELAKIS, G. GRAMMATIKAKIS

(Physics Dept , Unluerslty of Crete, Irakhon) and A. PAPADEROS (Orthodox Academy) Introductory words

17 30-18 30 M. ABLOWITZ Remarks on nonlinear evolu- tion equations (SO’)

19 00-2000 R. NEWTON Inverse scattering in three dimensions (50’)

Fnday, July 11 8 30-9 30 A. M. PERELOMOV Instanton-type solutions

m choral models (50’) 9 30-10 30 R. NEWTON Inverse scattering m three

dimensions (SO’) I I 00-12 00 Y. KODAMA Inverse scattering problems of

the finite depth fluid equation and the Ben- jamin-On0 equation (50’)

17 00-18 00. J. GREENE, D. HOLM and P MORRISON Canonical and noncanonical fluid dynamics (503

18 30-19 30 F. CALOGERO Isospectral matrices (50’)

Saturday, July 12. 8 3&9 30 J GREENE and I. C. PERCIVAL Regular

and Irregular motion m the complex plane (50’)

9 3&1000 F. ESTABROOK Sohtons and antisolitons

(25’) IO 30-1130 N. IBRAGIMOV and A B SHABAT L-A

paus and an mfimty of L-B groups and m- tegrals for nonlinear evolutron equations (50’)

17 00-18 00 R. K. BULLOUGH Some problems-apphc- able and mapphcable (50’)

18 30-19 00 T. BOUNTIS Periodic solutrons and chaos m Harmltoman systems (25’)

19 00-19 30 R. CONTE On the mtegrablhty of a four- vortex system (25’)

21 15-22 15 F. KARABASI (Orthodox Academy) Intro- duction to byzantme architecture (with slides) (503

Sunday, July 13 10 30-11 30 A. PAPADEROS (Director, Orthodox

Academy) Introduction to the Orthodox Academy (50’)

17 00-18 00 J. HONERKAMP Quantlzatlon of exactly m- tegrable field theoretical models (SO’)

18 30-19 30 L D FADDEEV and P. KULISH Develop- ment of the quantum inverse problem method (50’)

Monday, July 14 6 30-23 00 Excursion to the Samarra gorge

Tuesday, July 15 8 30-9 00 H. M. ZHANG Nonclassical variations field

theory (30’) 9 00-10 00 Li Yi SHEN Elgenvalue problems, the struc-

ture equation of Lie groups and some evolu- tion equations (503

10 30-11 00 M. BOITI Nonlinear evolution equations sol- vable by spectral transform and Backlund transformations of Weierstrass and Pamlevt transcendents (25’)

11 00-11 30 P. CAUDREY The inverse problem for the ‘third order equation urrx + q(x)ul + r(x)u = - @u (25’)

17 O&-l8 30 POSTER SESSION A. AROSIO* Asymptotic behavlour as t + CC of solutions of hnear hyperbolic equations with coefficients chscontmuous m time on a boun- ded domain M. BRUSCHI and 0. RAG- NISCO Nonlinear evolution equations, Back- lund transformations and generalized Lax technique J. C. EILBECK A model for pat- tern formation m biological systems D. HOLM. Hamilton-Cartan structure of fluid dynamics F PIRANI, M. LEO, R. A LEO, L. MARTINA and G. SOLIANI Algebraic pro- perties of nonlinear evolution equations

18 30-19 30 G. CASATI Energy transport m nonlinear systems (SO’)

21 15-22 15 T. SCHNEIDER and E STOLL Classical sta- tistrcal mechanics of sohton-bearing systems (with films) (SO’)

Wednesday, July 16 8 30-9 30 B. KUPERSCHMIDT Integrable systems

depending upon a functional parameter (50’) 10 00-10 35 P. SODANO Sohtons in quantum field theory

(30’)

Francesco Calogero and Andonrs Verganelakrsl Workshop on dynamrcal systems 547

10 35-11 10 L MERCALDO, I RABUFFO and G. VITIELLO Canomcal transformations m QFT and the sohton solutions (30’)

16 00-17 00 S. MANAKOV Integrable equations in 2 + 1 dimensions and a nonabehan Radon transform

(50’) 17 00-17 30 D. LEVI Backhmd transformations and non-

linear dlfferentlal-difference equations (25’) 17 30-18 00 P. M. SANTINI Asymptotic behavlour of

solutions of the cyhndrlcal KdV equation and of the Kadomtsev-Pyatlashvlh equation (25’)

18 30-19 30 M. BRUSCHI Nonlinear dlfferentlal- difference evolution equations and Backlund transformations associated with the discrete matrix Schrodmger spectral problem (25’) and 0. RAGNISCO Discrete analogue of the matrix Schrodmger spectral problem (25’)

21 15-22 15 F. KARABASI: Introduction to the Minoan archaeologlcal site m Knossos (with shdes) (50’)

Thursday, July 17 7 00-24 00 Excursion to Knossos and partlclpatlon to the

festlvltles of Aghta Marma

Friday, July 18

17 00-18 00 S. AUBRY Ground state of modulated struc- tures and stochastlclty (50’)

18 30-19 30 A. FORDY Nonlrnear Klem-Gordon equa- tlons and simple Lie algebras (50’)

8 30-9 30 V. G. MAKHANKOV Many-dImensIona SOII-

tons and pulsons, Isotopic structure and m- tegrablhty of systems of coupled Schrodmger equations (50’)

10 O&l 1 00 J. D. GIBBON Two examples of the Lorentz equations for dlsperslvely unstable systems and a connection with the sine-Gordon equa- tion (SO’)

Saturday, July 19 8 30-8 50 C. POPPE Degenerate sohton solutions of the

sme-Gordon equation (15’) 8 50-1100 M. SATO, T. MIWA and M. JIMBO

Monodromy preservmg deformation of linear dlfferentlal equations with Irregular smgularl- ties and the theory of T-functions (100’)

16 00-17 00 A. FOKAS Symplectic operators, theu Back- lund transformations and hereditary sym- metries (50’)

1700-1800 P. WEDER Some mathematical problems of Yang-Mdls equations (SO’)

18 30-19 30 D. A. UHLENBROCK Solution of the quanta1 Luttmger model (50’)

21 15-22 45 FILMS by C. EILBECK NumerIcal solutions of the Regularized Long Wave equation, Some solutions of nonhnear Klem-Gordon equa- tlons, Zoomerons, Two-dImensIonal sohtons, Davydov solutions on the a-hehx, Pattern

formation m coupled nonlinear evolution equations

Sunday, July 20 10 30-11 20 R. D. PARMENTIER Sme-Gordon system

with dlsslpatlon and bias the long Josephson tunnel junction (40’)

11 20-l 1 40 H. M. ZHANG On the acceleration of a single electron m the electromagnettc field (15’)

11 40-12 00 W. MALFLIET A solution method for some nonhnear evolution equations (15’)

17 00-18 00 P. SABATIER On water waves produced by ground motions (SO’)

18 30-19 30 D. ATKINSON On certam very singular m- tegral equations (503

Monday, .luly 2 1 8 30-9 20 P. L. CHRISTIANSEN Sme-Gordon sohtons

on Josephson hnes and m 2 + 1 and 3+ 1 dlmenslons (40’)

9 20-9 40 P. LOMDAHL NumerIcal solution of sohton problems (15’)

1000-11 00 P. B. KAHN and J LIN Turbulence m one- dImensIonal dlfferentlal-delay dlffuslon equa- tlons (50’)

15 00-16 00 J. GIBBONS Integrable colhslonless Boltz- mann equations (50’)

1600-1700 M. D. KRUSKAL On trymg to pursue the analogy between the KdV and BenJamm-One equations (50’)

18 30-24 00 Vlslt to Chama and concert by Mlkl Theodorakls

Tuesday, July 22 8 30-9 30 A. DEGASPERIS Abstract nonhnear evolu-

tlon equations and Lie algebras (50’) 10 O&l 1 00 II. SEGUR Two problems m nonlmear waves

(50’) 17.00-18 00 Summary and dIscussIon

Wednesday, July 23 Departure of partlclpants

3. List of participants

M J ABLOWITZ, Clarkson College, Potsdam, N Y 13676, USA

A AROSIO, Ist~tuto dr Matematrca dell’Unwersltci dl Plsa, Italy

D ATKINSON, Institute for TheoretIcal Physrcs, Gronm- gen, The Netherlands

S AUBRY, Laboratowe Leon Bnlloum, Glf-sur-Yoette, France

M BOITI, Ist~tuto dl Asrca de/l’Umuers& dl Lecce, Italy T BOUNTIS, Clarkson College, Pots-dam, NY 13676,

USA

548 Francesco Calogero and Andoms Verganelakisl Workshop on dynamtcal systems

M BRUSCHI, Istttuto dt Ftstca dell’Unmerstt6 dt Roma, V. G MAKHANKOV, Joint lnstttute for Nuclear Research, Italy Dubna, USSR

R K BULLOUGH, The Unruersrty of Manchester, Instttute of Scrence and Technology, U K

F CALOGERO, Istttuto dt Fistca dell’Untuerstt& dt Roma, Italy

S V MANAKOV, L D Landau Instttute for Theorettcal Phystcs, Moscow, USSR

L MARTINA, Jstttuto Nazronale dr Ftsrca Nucleare, Roma, Italy

G CASATI, Jstttuto dt Ftstca dell’Umuersrtd dr Mdano, Italy

L MARTINEZ ALONSO, Untuerstdad Complutense de Madrid, Spam

P J CAUDREY, The Umuerstty of Manchester, Instrtute of Sctence and Technology, U K

R CONTE, Centre d’Etudes Nucleatres de Saclay, Gtf -sur- Yuette, France

P L CHRISTIANSEN, The Techmcal Umuerstty of Den- mark, Lyngby, Denmark

G P MCCAULEY, The Unruersrty of Btrmmgham, U K T MIWA, RIMS, Kyoto Unruersrty, Japan Y MORI SATO, RIMS, Kyoto Unmerstty, Japan R G NEWTON, Indtana Unruersrty, Bloommgton, USA R D PARMENTIER, Istnuto dt Ftstca dell’I.Jntuersttd dt

Salerno, Italy H M A de CASTRO, Instttuto de Ftstca de Unmerstdade de

Sao Paulo, Brazil F PEMPINELLI, Istltuto dr Ftsrca dell’llmuersrtd dt Lecce,

Italy A DEGASPERIS, Istttuto dt Rstca dell’Umtersttb dt

Roma, Italy I C PERCIVAL, Queen Mary College, Umuersrty of Lon-

don, UK P DHOOGHE, Kath Untuersrtett Leuuen, Belgium J C EILBECK, Hertot-Watt Umuersrty, Edinburgh, Scot-

land F B ESTABROOK, Caltech, Pasadena, USA N FLYTZANIS, Unmerstty of Crete, Irakhon, Greece A S FOKAS, Clarkson College, Potsdam, N Y 13676, USA A FORDY, Unruerstty College, Dublin, Ireland J D GIBBON, Unmersrty College, Dublin, Ireland J GIBBONS, Umuerstty College, Dublin, Ireland J M GREENE, Plasma Phystcs Lab, Pnnceton, NJ, USA F GUIL GUERRERO, Unruerstdad Complutense de

Madrid, Spam

A M PERELOMOV, Instttute of Theoretical and Expert- mental Phystcs, Moscow, USSR

C POPPE, Unruersttat Heidelberg, Germany 0 RAGNISCO, Istituto dt Ftstca dell’Unmerstta dt Roma,

Italy H SABATA, Kyokru Universrty, Osaka, Japan P C SABATIER, Umu Set et Tech du Languedoc,

Montpellrer, France P M SANTINI, Jstttuto dr Ftstca dell’l_Jnmersttic dr Roma,

Italy

D D HOLM, Los Alamos Scienttfic Laboratory, New Mexico, USA

J HONERKAMP, Umuerstty of Fretburg, Germany N J IBRAGIMOV, USSR Academy of Sciences, Stbertan

Branch, Nouostbtrsk, USSR M JIMBO, RIMS, Kyoto Untuerstty, Japan P B KAHN, SUNY, Stony Brook, N Y, USA Y KODAMA, Clarkson College, Potsdam, N Y, 13676,

USA

M SATO, RIMS, Kyoto Unruerstty, Japan T SCHNEIDER, IBM, Zurich, Switzerland H SEGUR, A R A P , Prmceton, USA Lt YI SHEN, Untuerstty of Science and Technology, Hofet,

People’s Republic of China P SODANO, Jstttuto dt Fistca dell’Unmersttci dt Salerno,

Italy G SOLIANI, Jstituto dt Ftstca dell’Untuersttd dt Lecce,

Italy

M D KRUSKAL, Prmceton Umuerstty, NJ, USA P KULISH, Academy of Sciences of the USSR, Lomr,

Lenmgrad, USSR B A KUPERSHMIDT, Umuerstty of Mtchtgan, Ann

Arbor, USA

E STOLL, IBM, Zurich, Swttzerland G THEODOROU, Umuerstty of Crete, Irakhon, Greece D A UHLENBROCK, Frete Unruersttat Berlin, Germany H VARVOGLIS, Untuerstty of Thessalomkt, Greece A VERGANELAKIS, N R C Demokrttos, Athens, Greece G VITIELLO, Istctuto dt Ftstca dell’tbnuersttb dt Salerno,

Italy

P A LAGERSTROM, CALTECH, Pasadena, USA M LEO, Istttuto dt Ftstca dell’Untuerstta dt Lecce, Italy D LEVI, Istttuto dt Rstca dell’Umuersttd dt Roma, Italy P LOMDAHL, The Techmcal Umuerstty of Denmark,

W WESSELIUS, Twente University of Technology, Ens- chede, The Netherlands

Lyngby, Denmark W MALFLIET, Umuersttett Antwerpen, Wdrtlk, Belgium

S WOJCIECHOWSKI, Instttute of Theoretical Phystcs of the Untuerstty of Warsaw, Poland

P WEDER, JIMA& UNAM, Mexico City, Mexico H M ZHANG, Jman Umuerstty, Shandong, People’s

Repubhc of Chma