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Zakharov V.E. — What is integrability?
Zakharov V.E. — What is integrability?

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Название: What is integrability?

Автор: Zakharov V.E.

Аннотация:

This monograph deals with integrable dynamic systems with an infinite number of degrees of freedom. Leading scientists were invited to discuss the notion of integrability with two main points in mind: 1. a presentation of the various recently elaborated methods for determining whether a given system is integrable or not; 2. to understand the increasingly more important role of integrable systems in modern applied mathematics and theoretical physics. Topics dealt with include: the applicability and integrability of "universal" nonlinear wave models (Calogero); perturbation theory for translational invariant nonlinear Hamiltonian systems (in 2+1d) with an additional integral of motion (Zakharov, Schulman); the role of the Painlevé test for ordinary (Ercolani, Siggia) and partial differential (Newell, Tabor) equations; the theory of integrable maps in a plane (Veselov); and the theory of the KdV equation with non-vanishing boundary conditions at infinity (Marchenko).


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 321

Добавлена в каталог: 10.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action-angle variables      213ff
AKNS hierarchy      98
Algebraic manipulation program      8
Applicability      1 14
Augmented manifold      68
Augmented phase space      65
Backlund transformations      76
Balances      66
Billiard      264ff
Billiard in quadrics      252
Boussinesq equation      27
Branches      81
Burgers equation      36
Burgers equation, generalized      34 37
Burgers hierarchy      38
Burgers type equations      129ff 135ff
C-integrable      1ff 116
C-integrable equations      3ff
Canonical densities      151
Canonical potentials      155
Carrier wave      8 14
Cauchy problem      273
Cell decomposition      105
Classical symmetries      116
Classification      132
Classification of integrable equations      115 176
Closure      291
Cole — Hopf transformation      142
Commuting correspondence      261
Commuting mapping      251
Commuting mapping g      253
Commuting rational mappings      257 258
Complex Lie algebra G      257
Condition for integrability      18
Conservation laws      146
Conserved density      131
Constructive technique      14
Contact transformations      125
coupled equations      159
Cylindrical KdV      27
Cylindrical NLS equation      27
Davey — Stewartson equation      see “DS”
Davey — Stewartson-type equations      230ff
Decreasing initial conditions      187
Degenerative dispersion laws      193ff
Differential substitutions      179
Discrete analog of the Moser — Trubowitz formalism      252
Discrete analog of the Neumann problem      252
dispersion      3
dispersion relation      23
Dispersive      4 5 7 13
Dominant mode      7
DS      28 186 230
Duffing oscillators      106
Dynamic system with discrete time      261 262
Eckhaus equation      17 41 42
Ellipsoidal billiard      268
Elliptic example      67
Euler — Chasles correspondences      260
Fifth order scalar equations      159
Finite-difference equations      13
Formal diagonalization      152
Fourier asymptotic expansion      7
Galileian transformation      117
Generalized Burgers equation      34
Generalized higher Burgers equations      37
Global theorem      203
Group velocity      4 5
Hamilton — Jacobi equation      67
Hamiltonian theory      261
Harmonics      22
Heat equation      34
Heisenberg chain      252 263
Henon mapping      259
Henon — Heiles system      90
Higher symmetries      116
Hirota equation      25 88
Holstein — Primakov variables      235
Infinite dimensional dynamical systems      123
Integrability      1 14 63 73 185
Integrability conditions      158
Integrable mapping      251ff
Integrable maps      253 256
Integrable polynomial      252
Integrable rational mappings      257
Integrals of motion      209
Integrodifferential equations      13
Invertible quadratic mappings      259
Kadomtsev — Petviashvili equation      see “KP”
KdV      26 75 76 81 117 143 273
KdV hierarchy      86 98
Key to integrability (table)      54
Kink-like solution      35
Klein — Gordon equation      128
Korteweg — de Vries equation      see “KdV”
kp      28 119 186 220 227ff
Lagrangean systems with discrete time      251
Lax pair      15 28 85
Lax — Manakov matrix form      32
Lax — Manakov triad      31
Lie algebra      124 251
Lie symmetries      142
Linear Schrodinger equation      14
Linear spectral problem      24
Linearization      139
Liouville equation      46
Liouville integrability      65
Liouville theorem, discrete analogue      262
Liouville’s torus      262
Local conservation laws      121
Local uniqueness theorem      202
Lorenz equations      75 106 110
Maccari      3
Matrix DS equation      31
Matrix KdV equation      28
Matrix KP equation      30
Matrix NLS equation      28
Mikhailov and Shabat example      97
Modified Korteweg — de Vries equation      26
Modulation      7 14
Moser mapping      259
Necessary conditions for integrability      2
NLS      2 13 28
Non-decreasing initial data      273
Non-truncated expansions      89
Nonlinear pdes      1
Nonlinear Schrodinger equation      see “NLS”
Normal form      215
Not C-integrable      18
Not S-integrable      18
ODE integrability      65
Painleve equation      74
Painleve property      63
Painleve test      80
Painleve’ approach      59
Painleve’ branches      97
Painleve’ expansions      95
Perturbation theory      185
Perturbed wave equation      23
Poincare theorem      193ff
Polynomial Cremona mappings      251
Polynomial mapping      251 254 256
Properties of asymptotic states      205
psi series      82
Rational mappings      251
Rational solutions      95
Reflectionless potentials      276 282 284
Regular solutions      73
Rescaling      3 13
Resonance      22 67 82
Riccati example      65
S-integrable      1ff 116
Scattering matrix      187
Schrodinger operator      273
Schrodinger type equations      173
Separability      70
Simple complex Lie algebra      253
Sine-Gordon equation      6 14
Sinh-Gordon equation      15 30
Slow variables      8 18
Soliton solution      35 36
Spectral theory of difference operators      267
Spherical KdV      27
Stability      14
Symmetrical equations      174
Symmetrical transformations      174
Symmetry approach      115
Symmetry of PDE      117
Symplectic mapping      258
Taniuti      3
Tau function      87
Toda lattice      99
Transformations      124
traveling wave      4 7
Truncated expansions      89
Universal character      17
Universal method      222
Universal model equations      2
Universal nonlinear PDEs      57
Vector equation      152
Veselov — Novikov equations      227ff
Wave modulation      5
Wave packet      4 5
Weak nonlinearity      2 5 6
Weiss, Tabor, and Carnevale      see “WTC”
Weyl functions      286ff
Weyl solutions      286
WTC      80
WTC method      81 84ff
Yang — Baxter equation      260
Zakharov class      29
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