Dickey L.A. — Soliton Equations and Hamiltonian Systems :: Электронная библиотека попечительского совета мехмата МГУ

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Dickey L.A. — Soliton Equations and Hamiltonian Systems

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Название: Soliton Equations and Hamiltonian Systems

Автор: Dickey L.A.

Аннотация:

Dickey (mathematics, U. of Oklahoma) provides a detailed description of solitons, which have numerous applications in mechanics and physics. The new edition contains several additions and modifications including discussion of the Zakharov-Shabat matrix hierarchy with rational dependence on a spectral parameter, and its relationship to isomonodromic deformations. Overall, the emphasis of the second edition is on hierarchies of integrable equations rather than individual equations. The second edition also contains a new preface by the author. Chapters include Hamiltonian structure of the GD hierarchies, Kupershmidt-Wilson Theorem and modified KdV and GD, and tau functions of matrix hierarchies.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2003

Количество страниц: 350

Добавлена в каталог: 29.03.2008

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Предметный указатель

"Quasi primary" field      253
$w_{\infty}$ -algebra      267
$\tau$ -function      97
$\tau$ -function for AKNS-D      206
$\tau$ -function from the Grassmannian      126
$\theta$ -function      138
Abel, differential      137
Abel, mapping      135 137
Action-angle variables      308
Additional symmetries      113
Adler mapping      19
Adler — Gelfand — Dickey (AGD) algebra      48
Algebraic-geometrical solutions      132
Baecklund transformation      71 73 215
Baecklund — Darboux transformation      73
Baker      91
Baker function from the Grassmannian      125
Baker — Akhiezer      91
Baker — Akhiezer — Krichever lemma      135
Bilinear identity      92
Boussinesq equation      13
Characteristic of the first integral      273
Classical $W_{n}$ -algebra      251
Clifford algebra      106
Coadjoint representations      34
Coordinate-momentum variables      33 348
Differential Fay identity      102
Dressing      89
Drinfeld — Sokolov reduction      154
Euler — Lagrange equation      30
Exactness of the bi-complex      336
Faa di Bruno polynomials      81 101 111
Fay identity      102
Field theory, energy-momentum tensor      346
Field theory, Lagrangian      346
Field theory, Poisson bracket      356
Field theory, symplectic form      346
Field theory, variational derivatives      342
First integral      14
First structure      47
Fock representation      106
Gardner — Zakharov — Faddeev — Poisson bracket      41
Genus of the Riemann surface      298 312
Grassmannian      124
group characters      240
Hamilton mapping      28
Hamiltonian      26
Hamiltonian mapping      47
Hamiltonian mapping for AKNS-D      147
Hamiltonian mapping for KP      83
Hamiltonian of infinitesimal diffeomorphism      256
Hamiltonian pair      52
Hamiltonian structure of stationary equations      303
Hamiltonians of the AKNS-D      151

Hamiltonians of the KP hierarchy      87
Hierarchy, AKNS-D      141
Hierarchy, GD      13
Hierarchy, general matrix      195
Hierarchy, KdV      13
Hierarchy, KP      75
Hierarchy, modified KP      216
Hierarchy, multi-pole      173
Hierarchy, q-KP      224
Hierarchy, single-pole      165
Isomonodromic deformations      187
Kontsevich integral      250
Korteweg — de Vries equation (KdV)      13
KP equation      76
KP hierarchy      75
KP hierarchy, constrained      218
KP hierarchy, discrete      222
Kupershmidt and Wilson theorem      68
Lax pair      12
Liouville integration      284
Magri's Poisson bracket      42
Miura transformation      67
Miwa transformation      240
Modified GD      73
Modified KdV equation      71 147
Nonlinear Schroedinger equation      146
Normal ordering      103
Poisson bracket      26 84
Poisson bracket for AKNS-D      149
Poisson bracket for KP      84
Poisson — Lie — Berezin — Kirillov — Kostant bracket      36
Primary field      253
Primary generators of the $W_{n}$ -algebra      258
Principal chiral field      384
Principal chiral field equation      177
Pseudodifferential operators $(\Psi DO)$       10
Resolvents      18
Rotation of the n-dimensional rigid body      323
Schouten bracket      28
Schur polynomial solutions      237
Second structure      47
Soliton-type solutions      16
Stabilizing chain      231
Stationary equations of the KdV hierarchy      278
Stationary equations of the matrix hierarchy      295
String equation      119
Symplectic form      25 29 35
Tulczyjev's operator      337
Universal property of KP      94
Variational bi-complex      331
Variational bi-complex of a differential equation      350
Variational derivative      9
Vertex operator      103
Virasoro algebra      44

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