Introduction to Classical Integrable Systems

Front Cover
Cambridge University Press, Apr 17, 2003 - Mathematics - 602 pages
This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

I
6
II
6
V
7
VI
10
VII
11
VIII
13
IX
17
XI
19
LXXXVII
282
LXXXVIII
290
LXXXIX
299
XCII
303
XCIII
308
XCIV
311
XCV
314
XCVI
316

XII
20
XIII
22
XIV
23
XV
25
XVI
27
XVII
32
XIX
33
XX
35
XXI
41
XXII
49
XXIII
54
XXIV
59
XXV
62
XXVI
65
XXVII
72
XXVIII
74
XXIX
79
XXX
86
XXXII
89
XXXIII
92
XXXIV
94
XXXV
96
XXXVI
97
XXXVII
100
XXXVIII
105
XXXIX
109
XL
115
XLI
124
XLII
125
XLIII
130
XLIV
138
XLV
142
XLVI
145
XLVII
149
XLVIII
153
XLIX
154
L
156
LI
162
LII
164
LIII
167
LIV
169
LV
175
LVI
178
LVII
181
LVIII
182
LIX
184
LX
191
LXI
193
LXII
196
LXIII
200
LXIV
206
LXVI
208
LXVII
210
LXVIII
214
LXIX
216
LXX
218
LXXI
220
LXXII
221
LXXIII
223
LXXIV
226
LXXV
232
LXXVI
239
LXXVII
244
LXXVIII
249
LXXIX
251
LXXX
262
LXXXI
264
LXXXII
270
LXXXIII
272
LXXXIV
277
LXXXV
278
LXXXVI
280
XCVII
322
XCVIII
328
XCIX
331
C
338
CII
341
CIII
344
CIV
348
CV
352
CVI
355
CVII
359
CVIII
363
CIX
364
CX
370
CXI
379
CXII
382
CXIV
386
CXV
392
CXVI
394
CXVII
398
CXVIII
408
CXIX
414
CXX
419
CXXI
425
CXXII
433
CXXIII
443
CXXIV
445
CXXV
447
CXXVI
454
CXXVII
456
CXXVIII
463
CXXIX
467
CXXX
471
CXXXI
474
CXXXII
481
CXXXIII
486
CXXXVI
487
CXXXVII
496
CXXXVIII
497
CXXXIX
498
CXL
502
CXLI
505
CXLII
510
CXLIII
516
CXLV
522
CXLVI
525
CXLVII
532
CXLVIII
534
CXLIX
538
CL
540
CLI
542
CLII
545
CLIII
547
CLIV
549
CLV
551
CLVI
553
CLVII
554
CLVIII
556
CLIX
559
CLX
560
CLXI
562
CLXII
563
CLXIII
567
CLXIV
568
CLXV
571
CLXVII
574
CLXVIII
580
CLXIX
583
CLXX
587
CLXXI
592
CLXXII
599
Copyright

Other editions - View all

Common terms and phrases

About the author (2003)

Olivier Babelon has been a member of the Centre National de la Recherche Scientifique (CNRS) since 1978. He works at the Laboratoire de Physique Théorique et Hautes Energies (LPTHE) at the University of Paris VI-Paris VII. His main fields of interest are particle physics, gauge theories and integrables systems.

Denis Bernard has been a member of the CNRS since 1988. He currently works at the Service de Physique Théorique de Saclay. His main fields of interest are conformal field theories and integrable systems, and other aspects of statistical field theories, including statistical turbulence.

Michel Talon has been a member of the CNRS since 1977. He works at the LPTHE at the University of Paris VI-Paris VII. He is involved in the computation of radiative corrections and anomalies in gauge theories and integrable systems.

Bibliographic information