Introduction to Classical Integrable Systems

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Cambridge University Press, Apr 17, 2003 - Mathematics - 602 pages
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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.
  

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Contents

II
1
III
5
V
7
VI
10
VII
11
VIII
13
IX
17
XI
19
LXXXII
282
LXXXIII
290
LXXXIV
299
LXXXV
303
LXXXVI
308
LXXXVII
311
LXXXVIII
314
LXXXIX
316

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

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