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Wang D. (ed.), Zheng Z. (ed.) — Differential Equations with Symbolic Computations
Wang D. (ed.), Zheng Z. (ed.) — Differential Equations with Symbolic Computations

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Название: Differential Equations with Symbolic Computations

Авторы: Wang D. (ed.), Zheng Z. (ed.)

Аннотация:

This book presents the state of the art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions. The 20 chapters are written by leading experts and are structured into three parts.

The book is worth reading for researchers and students working on this interdisciplinary subject but may also serve as a valuable reference for everyone interested in differential equations, symbolic computation, and their interaction.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 374

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\lambda$-homogeneous      309
Abel      57
Abel differential equation      57 59
Algebraic critical      146
Algebraic differential equation      201
Algebraic genus      204 208
Algebraic limit cycle      55
Algebraic multiplicity      146
Algebraic resultant      333
Algebraic singular point      124
Algebrico-differential equations      343
Algebrico-differential polynomial      345
Algorithm for Finding Time-Reversible Systems      81
Analytic equalities      86
Analytic equality      95
Ascending set      344
Attractive region      121
Autoreduced      354 356
Bamon      55
Basic set      344
Bautin      27
Bautin ideal      72
Beke      239
bi-Hamiltonian      308
Bifurcation      1 121
Bifurcation at infinity      2
Binary invariant      76
Bouquet      201
Boussinesq equations      320
Briot      201
Bruno, A.D.      173
Burgers      308
Burgers equation      297
C-integrability      319
C-integrable      308 320
Carleman linearization method      174
Carnicer, Manuel M.      144
Carnicer’s theorem      144
Center      4 23 24 37 71 160
Center problem      67
Center variety      24 72
Center-focus problem      159
Char-set      344
Characteristic functions      293
Characteristic number      76
Characteristic orbit      58
Characteristic set      344
Characteristic vector      76
class      344
Classical symmetry argument      5
Cofactor      143
Compatibility condition      346 349
Compatibility differential polynomial      343 346
Completed pol      358
Completed polset      358
Completely reducible partial differential system      217
Completion      354
Complex center      41
Complex isochronous center      41
Computer algebra      173 213
Condens.m      308
ConLaw      294
ConLaw1-4      308
Conservation law      255 261 281 291 307 310 317 319
Conservation law identity      294
Conservation law, discrete      281
Conservation laws      308 309 317 319—321
Conserved density      308 310—313 317 318 320
Conserved flux      310 316 317
CONSLAW      307—309 316—318 321
Constant      240
Coordinate      353
Coupled Korteweg — de Vries (cKdV) equations      258 259 260 262 273
Crack      299
Cyclicity      23
d-char-set      346
D-finite      215
D-finite system      213
Darboux function      56
Darboux integrable      56
Darboux polynomial      143
Darboux, Jean-Gaston      144
de Vries      307
Decomposable      241
Decomposable partial differential system      217
Degree      2 95
Degree-tuple      356
Degree-tuple-set      356
density      261 272
Density, discrete      281
Derivation      240
Devil problem      348
Dicriticality      146
Difference test      282
Difference, total      282
Differential characteristic set      346
Differential elimination      327
Differential elimination ideal      328 332
Differential extension field      244
Differential field      240
Differential Groebner basis      293
Differential ideal      351
Differential module      239 240
Differential resultant      327 333
Differential submodule      239
Differential zero-decomposition theorem      343
Differential-difference equation      279
Differential-difference equations      308
Dilation, invariant      259 280
Dilation, symmetry      259 280
Direct sum      241
Displacement function      4
Divergence      263 264
Divergence free      257
Divergence test      5
Divergence, invert      268
Divergence, test      264 265
Divergence, total      261
Divergence-equivalent      270 272
Divisor      353
Down-shift operator      281
Drinfel’d — Sokolov — Wilson equations      319
Dual module      241
Duffing’s equation      181
Dulac’s theorem      2
Dynamic model      109
Dynamical system      85 173
Ecalle      55
Elimination ideal      329
Equilibrium      109
Equivalent      244 281
Equivalent differential systems      216
Eremenko      201
Euler operator      264 309 313 314
Euler operator, discrete      283 284
Euler operator, higher      265 266 283
Euler — Lagrange equation      309 313
Exactness      263
Exactness, criterion      265 282
Exactness, discrete      282
Exterior power      241
Factorization      213
Fast system      122
FGLM algorithm      32
Field of constants      215
Fine focus      4
First integral      55 59 67
First integral, Darboux      56 63
First integral, Liouvillian      60
First order algebraic differential equation      201
Flux      261 272
Flux, discrete      281
Focal value      160
Focal values      4
Focus quantities      71
Fold points      124
FORM      308
Forward difference invert      284
Forward difference operator      281
Frechet derivative      261
Fuchs      201
Fuchs conditions      208
Fuchs theorem      204
Fuchs’ conditions      202 204
Fuchs’s conditions      201
Gardner      308
Generalized 5th order KdV equation      316
Generalized differential resultant      327 334
Generalized differential resultant ideal      334
Generalized differential resultant system      327 334
Generalized NLS equations      299
Generalized resultant      327 330
Generalized resultant ideal      330
Generalized resultant system      330
Generalized symmetry      308
Global bifurcation      2
Goektas      308
Good basis      343 348
Groebner basis      32 347 351 352 360
Hamiltonian      308
Heisenberg algebra      308
Henon — Heiles’ system      185
Hereman      308
Heteroclinic orbit      3
Higher Euler operator, discrete      283
Higher than      353 355 357
Higher than, lower than, or identical to      356
Higher than, lower than, or incomparable to      356
hilbert      55
Hilbert numbers      2
Hirota — Satsuma system      258
Homoclinic orbit      3
Homotopy operator      255 267 268 270
Homotopy operator, discrete      284
Hopf bifurcation      123
Hyperexponential      244
Hyperexponential solution      239
Ilyashenko      55
Impasse surface      124
Implicit function theorem      123
Incremental computation      159
Infinite parameter conservation laws      291
infinity      38
Initial      344
Initial set      164
Integrability      55
Integrability condition      243 345
Integrability conditions      215
Integrability differential polynomial      343 346
Integrability testing      255
Integrable system      239 243
Integration of exact PDEs      293 299
Internal      241
Invariant algebraic curve      143
Invariant of the matrix group      74
Invariant symmetry      309
Invariants of the rotation group      75
InvariantsSymmetries      319
Inverse integrating factor      56 58 63
Involutive basis      347
Irrotational      257
Isochronous center      37
Isomorphism      241
IST      308
Ito equation      316 317 319
Kac — van Moerbeke (KvM) lattice      280 281
Kadomtsev — Petviasvili      304
Kamke      57
KdV equation      308 309
KK equation      316 317 319
Korteweg      307
Kovacic      202
Kovacic’s algorithm      205
Lagrangian      308
Lattice, Kac — van Moerbeke      280 281
Lattice, semi-discrete      279
Lattice, Toda      280 281 285
Lax equation      316 317
Lax pari      308
LCE      85
Leading coefficient      356
Leading degree-tuple      356
Leading monom      356
Leading term      356
Leading variable      95
Li      202
Liapunov quantities      24
Lie invariants      43
Lie — Euler operator      265 266 283
Lie — Euler operator, discrete      283
Lie-point symmetry      308
Lienard equation      1 6
LIMIT      159
Limit cycle      1 23 55 56 61
Limit cycle, algebraic      61 63
Linear differential equations      213
Linearization      291
Linearization of PDEs      291
Liouville      202
Liouville equation      294
Lisp      180
Local algebraic solution      146
Local analytic sets      177
Local bifurcation      2
Local families of periodic solutions      177
Local families of periodic solutions of the Henon — Heiles system      188
Lorenz system      85
Lotka — Volterra system      155
Lower than      353 355 357
Lueroth’s Theorem      203
Lyapunov characteristic exponent      85
Lyapunov function      4
Lyapunov number      115
Lyapunov quantity      5
M-part      359
M-pol      358
Maple      1 111 115 117 118 207 209 308
Mathematica      308
Mathematica system      180
mathscr ${E}_{i}(S)$      217
mathscr E(S)      217
MATLAB      1
Matsuda      201
Maximal LCE      85
Maximum      354
Membership problem      347
Miura      308
Modular algorithm      213
Monodromic singular point      58
Monom      356
Morphism      241
Movable critical point      202
Multiple      353
Multiple bifurcation      23
Multiple Hopf bifurcation      23
Multiplicativity      346 347
Multiplier      354
N-part      359
N-pol      359
Newton polygon      146
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