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Faddeev L.D., Takhtajan L., Reyman A.G. — Hamiltonian methods in the theory of solitons
Faddeev L.D., Takhtajan L., Reyman A.G. — Hamiltonian methods in the theory of solitons



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Название: Hamiltonian methods in the theory of solitons

Авторы: Faddeev L.D., Takhtajan L., Reyman A.G.

Аннотация:

The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schr?dinger equation, rather than the (more usual) KdV equation, is considered as a main example. The investigation of this equation forms the first part of the book. The second part is devoted to such fundamental models as the sine-Gordon equation, Heisenberg equation, Toda lattice, etc, the classification of integrable models and the methods for constructing their solutions.



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 597

Добавлена в каталог: 07.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$n$-soliton solution      135 171 383 429 497-498
$N$-wave model      309
$N$-wave model, $r$-matrix for      466
$N$-wave model, equation of      310
$N$-wave model, Hamiltonian for      311
$N$-wave model, Poisson structure of      311
$N$-wave model, zero curvature condition for      309-310
$r$-matrix      189 528
$r$-matrix, elliptic      537
$r$-matrix, rational      533
$r$-matrix, trigonometric      536
$r$-matrixfor the $N$-wave model      466
$r$-matrixfor the HM model      386
$r$-matrixfor the KdV model      467
$r$-matrixfor the LHM model      516
$r$-matrixfor the LL model      458
$r$-matrixfor the LLL model      508
$r$-matrixfor the LSG model      517
$r$-matrixfor the NS model      189
$r$-matrixfor the NS model, vector      466
$r$-matrixfor the SG model      433
$r$-matrixfor the Toda model      473
$r$-matrixfor the Toda model, two-dimensional      467
$S$-matrix, classical      246 393 444
$\check{Z}$ukowsky function      68
$\gamma$-ordered matrix exponential      23
$\Lambda$-operator      212 270 562
$\vec{n}$-field equation      328
$\vec{n}$-field equation, Hamiltonian for      328
Action for chiral field      312 322
Action for chiral field, modified      331
Action-angle variables finite density      253-258
Action-angle variables fortheHM model      338
Action-angle variables fortheNS model,rapidlydecreasing      229-232
Action-angle variables fortheSG model      435-437
Action-angle variables fortheToda model      503
Algebra of observables      13
Annihilator      20 325-326 510 524
Auxiliary linear problem      23 533
Auxiliary linear problem for continuous models      306-307
Auxiliary linear problem for lattice models      293
Auxiliary linear problem for the $LNS_{1}$ model      302
Auxiliary linear problem for the chiral field model      312
Auxiliary linear problem for the HM model      356
Auxiliary linear problem for the KdV model      308
Auxiliary linear problem for the LHM model      297
Auxiliary linear problem for the LL model      287
Auxiliary linear problem for the LLL model      511
Auxiliary linear problem for the NS model      23
Auxiliary linear problem for the SG model      393
Auxiliary linear problem for the SG model in light-cone variables      450
Auxiliary linear problem for the Toda model      475
Auxiliary linear problem, reflectionless      126
Auxiliary space      288 528
Averaging of fundamental Poisson brackets      538-539
Averaging of fundamental Poisson brackets of an $r$-matrix      533-538
Averaging of fundamental Poisson brackets on the lattice      542
Blaschke factor      50
Blaschke — Potapov matrix factor      92 380 426
boundary conditions      11
Boundary conditions, finite density      12 294
Boundary conditions, periodic      284
Boundary conditions, quasi-periodic      12 282 289 294
Boundary conditions, rapidly decreasing      11 282 285 294
Boundary conditionsin the sense of Schwartz      12
Breather      428
Brillouin zone      262 390
Canonically conjugate variables      230
Cartan — Weyl basis      466
Casimir function      524 529 544 552
Central extension      333 548
Charge      16
Chiral field equation      31 1
Chiral field equation, modified      331
Chiral field model      311-313 321-333
Chiral field model on a homogeneous space      313
Chiral field model, action for      312 322
Chiral field model, admissible functional for      326
Chiral field model, auxiliary linear problem for      312
Chiral field model, boundary conditions for      324 326
Chiral field model, Hamiltonian for      323 328
Chiral field model, modified      331-333
Chiral field model, Poisson structure of      322-329 332-333
Chiral field model, Poisson structure of, annihilator of      325-326
Chiral field model, principal      311-312
Chiral field model, zero curvature condition for      312
Coadjoint action      524 553
Cocycle      323 333 548
Compatibility condition      20
Condensation of zeros for the HM model      391
Condensation of zeros for the NS model      246-247
Condensation of zeros for the SG model      439
Condition ($A$)      49 362 400
Condition ($c$)      485
Condition ($\theta$)      69 149 254
Condition for the determination of signs      71 485
Conjugation problem      114-115 146-148
Connection coefficients      21
Conservation law      23
Continuous spectrum      49 56 477
continuum limit      298
Coupling constant      11
Current algebra      323 524
Current algebra, central extension of      333 548
Currents, left      311
Currents, right      323
Derivation property      188
Discrete spectrum      49 65 363 400-401 483
Dispersion law      243 262 390 438
Dispersion relation for the HM model      363
Dispersion relation for the NS model, finite density      68
Dispersion relation for the NS model, rapidly decreasing      51
Dispersion relation for the SG model      401
Dispersion relation for the Toda model      484
Divisor      334
Double soliton      428
Dressing procedure      336 555-558
Energy integral      16
Evolution equations for the Jost solutions      52 72 364 402 486
Evolution equations for the reduced monodromy matrix      52 73 364 402 487
Evolution equations for the transition coefficients      53 73 364 403 452 487
Evolution equations for the transition matrix      29 72 402 486
Evolution equations of Heisenberg type      29
Factorization of scattering      136 177 393 431
Factorization problem      546 552 559-560
Finite-gap solutions      268
Functional, admissible      18 75 209 235 237 239 326 369 499 505
Functional, inadmissible      19 260 283 369 390 505
Functional, local      33-34 364 487
Functional, multi-valued      292 330
Functional, real-analytic      13
Functional, smooth      13
Functional, with compact support      18 186
Fundamental Poisson brackets for the HM model      385-386
Fundamental Poisson brackets forlattice models      508
Fundamental Poisson brackets fortheLL model      458
Fundamental Poisson brackets fortheNS model      189
Fundamental Poisson brackets fortheSG model      433
Gap      57
Gauge equivalence      306 315
Gauge transformation      22 34 306 550
Gelfand — Levitan — Marchenko equation for the HM model      375
Gelfand — Levitan — Marchenko equation for the NS model, rapidly decreasing      116-117
Gelfand — Levitan — Marchenko equation for the NS model, rapidly decreasing, finite density      152-153
Gelfand — Levitan — Marchenko equationfor the Toda model      491
Gelfand — Levitan — Marchenko equationfor theSG model      416-417
Generating function for integrals of the motion      345
Generating function for integrals of the motion for the HM model      368
Generating function for integrals of the motion for the NS model      25 33-38 54 73
Generating function for integrals of the motion for the SG model      406
Generating function for integrals of the motion for the Toda model      487-488
Generating function of canonical transformation for soliton scattering for the HM model      392 393
Generating function of canonical transformation for soliton scattering for the NS model      244 245
Generating function of canonical transformation for soliton scattering for the SG model      444-445
Gohberg — Krein theorem      90
Goursat problem for the kernels $\Gamma_{\pm}$      359 397
Hamiltonian      15
Hamiltonian for the $LNS_{1}$ model      301
Hamiltonian for the $LNS_{2}$ model      304
Hamiltonian for the $N$-wave model      311
Hamiltonian for the $\vec{n}$-field model      328
Hamiltonian for the chiral field model      323 328
Hamiltonian for the chiral field model, modified      332
Hamiltonian for the HM model      283 390
Hamiltonian for the KdV model      309
Hamiltonian for the LHM model      296
Hamiltonian for the LL model      287
Hamiltonian for the LLL model      513
Hamiltonian for the LSG model      517
Hamiltonian for the NS model      16 19
Hamiltonian for the NS model, vector      288
Hamiltonian for the SG model      285
Hamiltonian for the SG model in light-cone variables      448
Hamiltonian for the Toda model      294
Hamiltonian for the Toda model, two-dimensional      313
Hamiltonian for the Volterra model      295
Hamilton’s equations of motion      15 545 551
Heisenberg magnet (HM) equation      281
Heisenberg magnet (HM) equation, higher      389
Heisenberg magnet (HM) model      281
Heisenberg magnet (HM) model, $n$-soliton solution for      383
Heisenberg magnet (HM) model, $r$-matrix for      386 387
Heisenberg magnet (HM) model, action-angle variables for      388
Heisenberg magnet (HM) model, admissible functional for      369
Heisenberg magnet (HM) model, auxiliary linear problem for      356
Heisenberg magnet (HM) model, boundary conditions for      282
Heisenberg magnet (HM) model, canonical variables for      388
Heisenberg magnet (HM) model, complete integrability of      388-389
Heisenberg magnet (HM) model, condition (A) for      362
Heisenberg magnet (HM) model, discrete spectrum in      363
Heisenberg magnet (HM) model, dispersion law for      390
Heisenberg magnet (HM) model, dispersion relations for      363
Heisenberg magnet (HM) model, fundamental Poisson brackets for      385-386
Heisenberg magnet (HM) model, gauge transformation of      315-321 391
Heisenberg magnet (HM) model, Gelfand — Levitan — Marchenko equation for      375
Heisenberg magnet (HM) model, Hamiltonian for      283 390
Heisenberg magnet (HM) model, higher equations for      389
Heisenberg magnet (HM) model, inadmissible functional for      283 369
Heisenberg magnet (HM) model, integrals of the motion for      366-368
Heisenberg magnet (HM) model, integrals of the motion for, generating function for      368
Heisenberg magnet (HM) model, interaction of solitons in      384
Heisenberg magnet (HM) model, inverse scattering problem for      370 372-373
Heisenberg magnet (HM) model, Jost solutions for      358
Heisenberg magnet (HM) model, Jost solutions for, analytic properties of      360
Heisenberg magnet (HM) model, Jost solutions for, asymptotic behaviour of      358 360-361
Heisenberg magnet (HM) model, Jost solutions for, evolution equations for      364
Heisenberg magnet (HM) model, Jost solutions for, integral equations for      359
Heisenberg magnet (HM) model, Jost solutions for, involutions for      358
Heisenberg magnet (HM) model, Jost solutions for, Poisson brackets of      386
Heisenberg magnet (HM) model, momentum for      283 292 320 390
Heisenberg magnet (HM) model, monodromy matrix for, reduced      361
Heisenberg magnet (HM) model, Poisson structure of      282 391
Heisenberg magnet (HM) model, Riccati equation for      365
Heisenberg magnet (HM) model, Riemann problem for      370-372
Heisenberg magnet (HM) model, scattering of solitons in      384 392-393
Heisenberg magnet (HM) model, scattering transformation for      393
Heisenberg magnet (HM) model, soliton for      379-381
Heisenberg magnet (HM) model, spin for      283 368-369 390
Heisenberg magnet (HM) model, trace identities for      368
Heisenberg magnet (HM) model, transition coefficients for      361
Heisenberg magnet (HM) model, transition coefficients for, analytic properties of      362-363
Heisenberg magnet (HM) model, transition coefficients for, asymptotic expansion of      368
Heisenberg magnet (HM) model, transition coefficients for, evolution of      364
Heisenberg magnet (HM) model, transition coefficients for, normalization condition for      361
Heisenberg magnet (HM) model, transition coefficients for, Poisson brackets of      387-388
Heisenberg magnet (HM) model, transition matrix for      357
Heisenberg magnet (HM) model, transition matrix for, asymptotic expansion of      364-365
Heisenberg magnet (HM) model, transition matrix for, involution for      358
Heisenberg magnet (HM) model, transition matrix for, Poisson brackets of      386
Heisenberg magnet (HM) model, zero curvature condition for      284 315
Hierarchy of Poisson structures      217-218 563-565
Hopf bundle      320
Integrability      307
Integral equations for the Jost solutions      44 359
Integral equations for the kernels $\Gamma$, $\bar{\Gamma}$      31
Integral equations for the transition matrix      30
Integral of the motion      16
Integral of the motion for the HM model      366-368
Integral of the motion for the LLL model      512 514
Integral of the motion for the NS model, finite density      73-76
Integral of the motion for the NS model, rapidly decreasing      53
Integral of the motion for the SG model      403-407
Integral of the motion for the SG model in light-cone variables      452 463
Integral of the motion for the Toda model      474 487-489
Integral of the motion in involution      17
Integral of the motion, local      33 364 512
Integral representations for $G(\lambda)$, $G_{\pm}(\lambda)$      85 86 140 144-145
Integral representations for $G(\lambda)$, $G_{\pm}(\lambda)$ for Jost solutions      41 57 359 397
Integral representations for $G(\lambda)$, $G_{\pm}(\lambda)$ for monodromy matrix      32 47 64
Involutions for $G(\lambda)$, $G_{\pm}(\lambda)$      84 86 140 141 371 408-409
Involutions for $G(\lambda)$, $G_{\pm}(\lambda)$ for Jost solutions      41 43 59 61 358 396 478
Involutions for $G(\lambda)$, $G_{\pm}(\lambda)$ for monodromy matrix      45 62 361 399 481
Involutions for $G(\lambda)$, $G_{\pm}(\lambda)$ for transition matrix      28 358 394-396
Jacobi identity      14 188
Jacobi matrix      479
Jost solutions for the HM model      358
Jost solutions for the NS model, finite density      57-58
Jost solutions for the NS model, rapidly decreasing      42
Jost solutions for the SG model      396
Jost solutions for the Toda model      477
Kadomtsev — Petviashvili equation      350
Killing form      321 527
Korteweg-de Vries (KdV) equation      307
Korteweg-de Vries (KdV) model      307
Korteweg-de Vries (KdV) model, $r$-matrix for      467
Korteweg-de Vries (KdV) model, auxiliary linear problem for      308
Korteweg-de Vries (KdV) model, Hamiltonian for      309
Korteweg-de Vries (KdV) model, momentum for      309
Korteweg-de Vries (KdV) model, Poisson structure of      308
Korteweg-de Vries (KdV) model, zero curvature representation for      307-308
Landau — Lifshitz (LL) equation      287
Landau — Lifshitz (LL) model      286 457
Landau — Lifshitz (LL) model, $r$-matrix for      458
Landau — Lifshitz (LL) model, auxiliary linear problem for      287
Landau — Lifshitz (LL) model, boundary conditions for      282
Landau — Lifshitz (LL) model, Hamiltonian for      287
Landau — Lifshitz (LL) model, limiting cases of      459-462
Landau — Lifshitz (LL) model, momentum for      292
Landau — Lifshitz (LL) model, Poisson structure of      458
Landau — Lifshitz (LL) model, zero curvature representation for      287 457
Lattice Heisenberg magnet (LHM) equation      296
Lattice Heisenberg magnet (LHM) model      296
Lattice Heisenberg magnet (LHM) model, $r$-matrix for      516
Lattice Heisenberg magnet (LHM) model, auxiliary linear problem for      297
Lattice Heisenberg magnet (LHM) model, boundary conditions for      296
Lattice Heisenberg magnet (LHM) model, continuum limit of      298
Lattice Heisenberg magnet (LHM) model, Hamiltonian for      296
Lattice Heisenberg magnet (LHM) model, partially anisotropic      516
Lattice Heisenberg magnet (LHM) model, Poisson structure of      296
Lattice Heisenberg magnet (LHM) model, zero curvature condition for      297
Lattice Landau — Lifshitz (LLL) model      508-515
Lattice Landau — Lifshitz (LLL) model, , $r$-matrix for      508
Lattice Landau — Lifshitz (LLL) model, ,zero curvature condition for      514
Lattice Landau — Lifshitz (LLL) model, annihilator for      510
Lattice Landau — Lifshitz (LLL) model, auxiliary linear problem for      511
Lattice Landau — Lifshitz (LLL) model, continuum limit of      515
Lattice Landau — Lifshitz (LLL) model, fundamental Poisson brackets for      508
Lattice Landau — Lifshitz (LLL) model, Hamiltonian for      513
Lattice Landau — Lifshitz (LLL) model, integrals of the motion for      512 514
Lattice Landau — Lifshitz (LLL) model, limiting cases of      515-518
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