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Clarkson P.A. — Applications of Analytic and Geometric Methods to Nonlinear Differential Equations
Clarkson P.A. — Applications of Analytic and Geometric Methods to Nonlinear Differential Equations



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Название: Applications of Analytic and Geometric Methods to Nonlinear Differential Equations

Автор: Clarkson P.A.

Аннотация:

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang — Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.

(ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang — Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.


Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 477

Добавлена в каталог: 06.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel equation      84 333 336 341
Abel mapping      38
Ablowitz, M.J.      8 15 16 25 81 87 108 161 181 215 239 251 256 270 280 313 322 339 351 404 438 439 453
Abramowitz, M.      322
Adler, R.      45
Airault, H.      351
Airy equation      310
AKNS equations      27ff 33 35—38
AKNS equations — 2+1-dimensions      68
AKNS operator      185
Akutsu, Y.      154
Alekseev, A.      181 182
Alonso, L.M.      429
Alonzo, L.M.      289
Andreev, V.A.      249
Anharmonic oscillator      441 451
Arimoto, S.      389
Ashtekar, A.      15
Athorne, C      192 228
Atiyah, M.F.      15 16 75 339
Atiyah— Ward ansatze      66
Avan, J.      181
B — Kadomtsev — Petviashvili (BKP) equation      13 148
Babelon      0. 181 182
Backlund transformation      115ff 183 186 217ff 223 227 231 241 242 244 245 247 257 258 265 266 268 289ff 297 300ff 309 310 318ff 332 342ff 348 351 352 412 415
Baker, J.A.      228
Bar Yaacov, D.      108 256
Barouch, E      351
Bartoclay, D.      313
Barzin, M.      45
Bassom, A.P.      315 322
Bateman, H.      228
Baumann, G.      388
Bazhanov, V.V.      154
Beals, R.      39 108
Bekki, N.      286
Belavin A.A.      8 108
Bellon, M.      313
Bender, C.M.      339
Benney equation      241 243
Benney, D.J.      192
Berezin, F.A.      138
Bernoulli equation      401 402
Bessel equation      310
Bessel function      341rT *347 348 351 352
Bianchi identity      241 244 246
Bianchi — IX equations      342
Bianchi, L.      249
Bluman, G.W.      339 363 373 388 413 429 439
Blumen, W.      228
Bobenko, A.      240
Bogdanov L.V.      108
Bogomolny equation      13
Boiti, M.      89
Bom M.      108 114 192 205 404
Bonora, L.      181
Bordemann, M.      240
Bouguenaya, Y.      80
Bouligand, G.      249
Boussinesq equation      262 282 375 376 395 415 417
Boussinesq, J.      429
Braid group      149
Brand, A.      373
Bretherton, F.P.      228
Brezi, E      313
Broer, L.T.F.      429
Bruschi, M.      181 228 239 240 438
Buchberger algorithm      151
Bullough — Dodd — Mikhailov (BDM) equation      217ff 222 223 226 227 241 342 409
Bullough, R.K.      256 413
Bureau, F.J.      280
Burgers' equation      81—87 291 294 367 372
Calogero, F.      87 108 114 122 138 239 240 373
Capel, H.W.      163 181 182 313 389 413 430 438 439
Cariello, F.      286 288 362 388
Carminati, J.      388
Carnevale, G.      280 286 362 404 430 390
Case, K.M.      249
Cauchy — Riemann equations      217 218
Caudrey. P.J.      429
Cellular automata      229—237
Chakravarty, S.      1 8 16 256 339
Champagne, B.      373 388
Chan, W.L.      138
Chandrasekhar, S.      351
Chau, L.L.      8
Chazy equation      15 272 276 331—337 341
Chazy V equation      277 278
Chazy, J.      280 339
Chen Dengyuan      138
Chen, D.-F.      389
Chen, H.H.      138
Chen, W.-Z.      389
Chen, Z.X.      388
Cheng, Y.      138
Chiral model      65 67 69
Chitre, D.M.      351
Chiu, S.C.      249
Chowdhury, A.R.      430
Chowdhury, S.R.      388
Chu, F.Y.F.      161
Chudnovsky, D.V.      286
Chudnovsky, G.V.      286
Clarkson — Kruskal direct method      375ff 380 383 385ff 395 397 398 403 405 411 415 417
Clarkson, P.A.      15 16 25 108 256 280 315 322 323 339 341 351 375 388 389 395 404 413 415 429 430
Classical Boussinesq (CB) equation      289—295 297 415 416
Claude, C      161
Cliiral equation      77ff 217 221
Coifman, R.R.      39 108
Cole, J.D.      87 388 413 429 439
Combescure transformation      243 247
Combs, J.A.      453
Conditional symmetry      375 405 411 412 425
Conformal group      11
Conservation laws      1 6 8 229 363
Conte, R.      271 280 281 286 288 298 362 429
Corrigan — Fairlie — t'Hooft — Wilczek ansatz      66
Corrigan, E.F.      39 75
Cosgrove, C.M.      388
Crum, M.M.      205
Crumey, A.D.W.B.      75
Curro, C      249
Cylindrical Korteweg-de Vries equation      135
D'Adda, A.      54
Damped Liouville equation      452
Darboux theorem      193 196 219
Darboux transformation      116 183—192 193- 217 218 356
Darboux, G.      192 205 228 249
Date, E.      181 205
Davey — Stewartson (DS) equations      6 8 15 74 89 91 105ff 111 112 147 183 202 207—215 217 251 395—404
Davey — Stewartson I (DSI) equation      91 103 105 207 209—214 395—397 399 403
Davey — Stewartson II (DSII) equation      91 103 105 207 210 211 395—397 399 401 403
Davey — Stewartson III (DSIII) equation      105 109 112 207 210—214
Davey, A.      192 404
Davis, H.T.      453
DBAR ($\overline\partial$) method      10 13 14 89 95 96 115 251
de Lillo, S.      81
Dee, G.      453
Degasperis, A.      115 122 138 239
Deift, P.      181 429
Delay Painleve equation      300 311 312
Demoulin, A.      249
Derivative nonlinear Scrodinger (DNLS) equation      315
Derivative nonlinear Scrodinger (DNLS) equation - 2 + 1-dimensions      68
Deser, S.      45
Devitt, J.S.      388
Di Vecciiia, P.      54
Dickey, L.A.      39
Differential Groebner bases      376 404
Diffusion convection equation      392
Discrete Korteweg — de Vries equation      299 302 432
Discrete Painleve equation      299—312 431
Dispersive long wave equation      342
Dispersive water-wave equation      416 417 429
Dixon, J.M.      453
Dodd, R.K.      352 413
Donato, A.      228
Dorizzi, B.      313
Double Sine — Gordon equation      452
Dressing method      3 4 7 27 28 33 34 36 37 69 186 202 203 217
Dressing orbit      33—37
Drinfel'd — Sokolov equation      12 27
Drinfel'd, V.G.      16 39 181
Dryuma, V.S.      228
Dubrovin, B.A.      215 240 249
Dubrovsky, V.G.      114 192 228
Dupin theorem      244 247
Eckhaus equation      110
Egorov coordinate systems      243 244
Egorov property      243 244 246
Egorov system      245
Egorov, D.Th.      249
Einstein / Yang — Mills equation      41—43
Einstein equation      9 10 15 77
Eisenhart, L.P.      249
Electromagnetic radiation      342
Elliptic equation      447 450 451
Elliptic function      238 304 342
Elliptic integral      443
Emden equation      441
Englefield, M.J.      391
Ernst equation      342
Espinosa, A.      388
Estevez, P.G.      287 289 388 429
Fackerell, E.D.      352 389
Faddeev, L.D.      16 181 182
Fairlie, D.B.      39 75 80
Fake Lax pair      137
Fay, J.      39
Fee, G.J.      388
Ferapontov, E.V.      249
Fitzhugh — Nagumo equation      376—383 385 387
Fitzhugh, R.      388
Flaschka, H.      298 351 429
Florianczyk, M.      429 453
Flytzanis, N.      270
Fokas, A.S.      87 108 215 239 240 256 313 351 352 404 439
Fordy, A.P.      228 271 280 286 339 362 413 429 439
Forgacs, P.      75
Fourier transform      115 253
Freeman N.C.      148 429
Fuchs — Painleve Test      272 276 353
Fuchs, R.      339
Fuchssteiner, B.      125 138 239 270
Fujioka, R.      388
Fusco, D.      161 249 439
Fushchlich, W.I.      388
Gabeskiria, M.A.      205
Gaeta, G.      388
Gaffet, B.      228
Gagnon, L.      404 429 453
Galaktionov, V.A      388
Gambier, B.      280 313 339
Ganesan. S.      404
Gauge group      5 12 14 15 65 67 68 74
Gel'fand — Levitan — Marchenko integral equation      115
Generalised Boussinesq equation      415—429
Generalised symmetries      356
Generalized nonlinear Scrodinger (GNLS) equation      427
Geogdzhaev, V.V.      249 298
Gervais, J.L.      182
Ghost equation      91 98 99
Ghost operator      95 101
Gibbons, J.      228 249 286 413 429
Gilson, C.R.      139 148 404 429
Goldberg, C.H.      239
Gordoa, P.G.      388 429
Gordoa, P.R.      287 289
Grammaticos, B.      192 299 313 404 413
Grinevic, P.M.      249 256
Groebner bases      151
Gromak, V.I.      313 351 429
Grundland, A.M.      453
Gunn, C.      240
Gunning, R.C.      39
Guo, B.-Y.      388
Guven, R.      351
Haar, A.      228
Haberman, R.      8 108
Halburd, R.G.      313
Hann, E.L.      161
Hansen, A.G.      429
Hardy, G.H.      148
Hastings, S.P.      351
Head, A.K.      373 388
Hearn, A.C.      154
Hereditary operator      128
Hereman, W.      373 388
Hicks, A.C.      315 322
Hietarinta, J.      153 192 313 413 439
Hill, J.M.      430 439
Hille, E.E.      351 362
Hirota bilinear form      70 139 142 146 183 190 191 257—270 281 289 291 295 294 380 387 397 416
Hirota derivative      139 141ff 191
Hirota formalism      291
Hirota, R.      148 181 270 298 313 430
Hitchin, N.J.      15 16 25 75
Hlavaty, L.      154
Hodge-star operator      2
Hodograph equation      217 218
Hohenberg, P.C.      286
Holomorphic vector bundle      3 10 13 14 17ff 21 23 35
Holomorphic vector field      69
Homographic transformation      278 279
Hood, S.      388 389 395 429
Hopf algebra      149 166
Hopf — Cole transformation      81 311 368
Hopf, E.      87
Horvath, Z.      75
Hoskins, B.J.      228
Huang, G.-X.      288
Hyper — Kaehler equations      17 18 23—25
Hyper — Kaehler geometry      14
Hypergeometric equation      272 310 331ff
Ince, E.L.      313 351 430 439 453
Inverse Laplace transform      84
Inverse scattering method (IST)      6 13 14 15 18 69 78 89 105 109 163 223 238 244 245 248 251 271 272 290 294 315 342 396 397 415 416
Ishimori equation      205
Ising model      342
Isomonodromy deformation method      17 18 23 299 309 342
Ito, M.      270
Its, A.R.      313 351 439
Itzykson, C.      313
Ivancovitch, J.S.      16
Iwasaki, K.      351
Izergin, A.G.      182
Jacobi variety      36
Jacobian elliptic function      176 377 378 383 384 400 415 417 421 422 424
Jacobson, T.      15
Jaulent M.      108 430
Jiang, Z.      239 256
Jimbo, M.      25 148 153 154 181 205 206 270 280 313 351
John, F.      75
Jones, P.      16
Joshi, N.      313 331 413 439
Jost solutions      115
Kac — Moerbeke lattice      231 232
Kac — Moody — Virasoro algebra      406 431 433 436
Kac — van Moerbeke equation      431—438
Kac, M.      240 439
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