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| Ïîèñê ïî óêàçàòåëÿì |
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| Sachdev P.L. — Nonlinear ordinary differential equations and their applications |
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| Ïðåäìåòíûé óêàçàòåëü |
Abel's equation 30 65
Abel's equation, relation to linear DE 30
Abel's formula 11
Asymptotic behaviour of nonlinear DE 151
Asymptotic series, operations with 122
Asymptotic series, solutions of a boundary layer problem - in terms of 122—127
Asymptotic solutions of cylindrical and spherical Burgers equation 516—519
Attractors, definition of 354
Attractors, strange 356
Autonomous DE 5
Bellman's equation 54
Benedixon's reduction 92
Binomial DE of first order 86
Blasius equation 56
Blasius equation, BVP for 217—218
Blasius equation, series solution with IC at infinity 99—100
Blasius equation, solution for BVP relating to 217
Bore over a sloping beach approximate treatment of 552
Bore over a sloping beach approximate treatment of, generalized similarity solution for 552—558
Bore over a sloping beach approximate treatment of, nonexistence of a self-similar solution 549—551
Bore over a sloping beach approximate treatment of, numerical solution for 549
Boundary layer equations, asymptotic series solution of BVP for 122—127
Boundary layer theory, BVP for 118
Boundary layer theory, BVP over an infinite domain 117—121
Boundary layer theory, equations of 117
Boundary value problems (BVP) 8
Boundary value problems (BVP), invariance of DE and 217
Boundary value problems (BVP), methods for existence of solutions of 213
Boundary value problems (BVP), number of possible solutions for 214
Boundary value problems (BVP), scaling and 217
Boundary value problems (BVP), shooting methods for 213 215—216
Boussinesq equation 427 428 431 434
Briot — Bouquet equation 88
Briot — Bouquet equation, equations reducible to 90—92
Briot — Bouquet equation, psi series solutions of 96
Briot — Bouquet equation, series solutions of 93—96
Briot — Bouquet equation, simple cases of 88—90
Briot — Bouquet equation, singularities of 88
Briot — Bouquet system and Pv 494—495
Burgers equation, plane N wave solutions of 514
Cauchy's majorant 111
Cavity collapse (spherical) of a uniformly moving cavity 318
Cavity collapse (spherical) of an accelerating cavity 318
Cavity collapse (spherical), phase plane analysis of 320—324
Cavity collapse (spherical), self-similar solutions describing 317
Chaotic solutions 352
Classification of singular points of linear DE 69
Combined k-dV equation 434
Contraction principle 227
Converging shock wave, global solutions for 529
Converging shock wave, Guderley's solution 534
Converging shock wave, trajectory of 532
Critical point 246
Dam break initial conditions 539—540
Deformation of a circular membrane BVP for 243—244
Degree of DE 3
Dirichlet series for BVP in boundary layer theory 118—121
Dominant behaviour of DE 140
Electromagnetic Theory, a DE arising in 231
Electromagnetic Theory, solutions of a BVP relating to 231—239
Elliptic PDE 2
Embedding of asymptotic solutions 164
Emden equation-phase plane analysis of 301
Emden — Lane — Fowler equation 54 60 61
Equidimensionality 24
Essential singularities 423
Euler — Painleve transcendents 187
Euler — Painleve transcendents, connection problems for 130 137
Euler — Painleve transcendents, Kamke's collection and 201—208
Euler — Painleve transcendents, Murphy's collection and 208—211
Euler — Painleve transcendents, other DE related to 200
Euler — Painleve transcendents, relation to GBE with damping 187—188
Euler — Painleve transcendents, series solution for 189 196
Euler — Painleve's equations 186 187
Existence of solutions of IVP 8
Factoring of nonlinear DE 42
Fisher's equation, IVP for 304
Fisher's equation, perturbation analysis of 307
Fisher's equation, phase plane study for travelling waves 306
Fisher's equation, steady-local analysis of 135—138
Fisher's equation, travelling wave solution of 304 305 306
Fixed singular point 420
Gas dynamic equations 2
General solution of a nonlinear DE 6 453
General solution of an nth order DE 7
Generalized Burgers equations (GBE) in cylindrical and spherical geometry 513
Generalized Burgers equations (GBE), N wave solutions of 516—519
Generalized Duffing equation 55
Gravity current releases, global solutions for 542—545
Gravity current releases, global solutions for, self-similar solutions for 541
Green's function for linear BVP 16—21
Hamiltonian systems, free end Toda lattice 411—413
Hamiltonian systems, Henon — Heiles 394—409
Hamiltonian systems, quartic lattice 409—411
Henon — Heiles system, integrability of and chaos in 394—409
Henon — Heiles system, Painleve analysis for 394—403
Homogeneous DE 3
Hyperbolic PDE 2
Index of a singularity 289
Indicial exponent 72
Inhomogeneous DE 3
Initial value problem (IVP) 7
Integrability of a quadratic second order system 419—420
Integrability of a quadratic third order DE 420
Integrability of DE 357—358
Integral equation formulation of BVP 175
Internal gravity waves 324
Inverse scattering transform 138
Irrational right hand sides, second order nonlinear DE with 452—454
Irrational right hand sides, singular solutions of DE with 453—454
Irregular singular point 74
Isothermal atmosphere, nonlinear periodic solutions and 326—327
Isothermal atmosphere, nonlinear travelling waves and 324
Iteration for nonlinear BVP 175
Iterative solutions for IVP 151—153
K-dV equation and PI 429 431
Kuramoto model-steady-singularities of and chaos in 413—418
Laminar boundary layer, BVP for 244
Laminar convection over a linear heat source, solution of BVP for 106
Langmuir — Blodgett equation 55
Langmuir — Boguslavski equation 55
Langmuir's equation 62
Laurent series 140
Levinson's method 154—158
Lindeloeff's majorant 112—116
Linear second order DE relation to nonlinear second order DE 37
Linearization (exact) of second order autonomous nonlinear DE 42
Linearly independent solutions 10
Local analysis of DE 131—132
Local analysis of DE - method of Painleve 132
Lorenz system, integrability of and chaos in 365—394
Lorenz system, integrable cases of 375—377
Lorenz system, numerical solutions of and singularities in 386—394
Lorenz system, Painleve analysis of 378—382
Lorenz system, perturbation analysis for periodic solutions of 368—374
Lotke — Volterra model, Painleve property of 361 364
Majorants 108
Majorants for first order DE 109—110
Majorants, Cauchy 111
Majorants, Lindeloeff 112—114
Malmquist theorem 96
Modified Koreteweg — de Vries equation and second Painleve equation 139 428 432
Movable singular points 422
N wave solutions 514
N wave solutions, cylindrical 517
N wave solutions, planar 514
N wave solutions, spherical 518
Natural convection with viscous dissipation, BVP for 244
Nature of singular point of two first order linear DE 256
Nature of singular point of two first order linear DE, center 258
| Nature of singular point of two first order linear DE, nodal star 259
Nature of singular point of two first order linear DE, node 256
Nature of singular point of two first order linear DE, saddle 257
Nature of singular point of two first order linear DE, vortex point 258
Nonharmonic oscillator, nonlinear 100
Nonlinear Bessel equation, asymptotic solution of 178—180
Nonlinear Bessel equation, BVP for 175
Nonlinear Bessel equation, integral equation formulation 178
Nonlinear Bessel equation, series solutions of 177
Nonlinear diffusion equation, BVP solution of, in the phase plane 314
Nonlinear diffusion equation, similarity solutions of 308
Nonlinear diffusion equation, study in the phase plane 309—314
Nonlinear PDE - solutions of - as infinite series 512
Nonlinear Schroedinger equation and Painleve equation 431
Nonsimple singular points for two-dimensional systems 273—284
Normal quadratic systems, applications of 287
Normal quadratic systems, classification of singular points for 292—301
Nth order system of DE, critical points of 246
Nth order system of DE, unique solution of 246
Order of DE 3
Ordinary point 69
Oregonator 361
Painleve's a-method 424
Painleve's fifth equation, Briot — Bouquet system and 494—495
Painleve's fifth equation, degenerate cases of 501
Painleve's fifth equation, radial wave equation and 497
Painleve's fifth equation, rational solutions of 499—501
Painleve's fifth equation, relation to PIII 498 501
Painleve's fifth equation, Riccati equation and 497
Painleve's fifth equation, solution about fixed singularities 493
Painleve's fifth equation, solutions with poles at zero 495—496
Painleve's first equation 460
Painleve's first equation and beyond 472
Painleve's first equation, asymptotic behavior for 468—469 466—467
Painleve's first equation, BVP 472
Painleve's first equation, IVP for 468
Painleve's first equation, numerical study of 469
Painleve's first equation, qualitative results for 470—472
Painleve's first equation, shooting techniques for 472
Painleve's first equation, solution as quotient of integral functions 471—472
Painleve's first equation, solution with movable poles 461—468
Painleve's fourth equation 482
Painleve's fourth equation, Hermite equation and 492
Painleve's fourth equation, rational solutions of 489 490—493
Painleve's fourth equation, solution as ratio of entire functions 483
Painleve's fourth equation, solution at infinity 488
Painleve's fourth equation, solutions with a simple movable pole 482
Painleve's fourth equation, systems related to 483—486 489—490
Painleve's property 138—139
Painleve's property, algorithm for testing a system of DE for 147
Painleve's property, algorithm for testing nth order DE for 140
Painleve's property, conjecture of Ablowitz, Romani and Segur 138
Painleve's second equation, Airy function and 476 480
Painleve's second equation, asymptotic analysis of 473 474
Painleve's second equation, connection problem for 475
Painleve's second equation, dependence of solution on amplitude parameter 475—478
Painleve's second equation, numerical study of 475 478—482
Painleve's second equation, relation to K-dV equation 474—475
Painleve's second equation, solution with movable simple pole 473 475
Painleve's second equation, Taylor series solution for 473
Painleve's second transcendent, asymptotic form 184—185
Painleve's second transcendent, connection problem for 181
Painleve's second transcendent, integral equation formulation for 183
Painleve's second transcendent, numerical solution of 183 185
Painleve's second transcendent, symmetries of 181
Painleve's sixth equation 424
Painleve's theorem for first order DE 84 85—86
Painleve's third equation 501
Painleve's third equation, asymptotic representation of solutions of 508—510
Painleve's third equation, expansions of solutions about zero 506—507
Painleve's third equation, perturbation solutions about unity 507
Painleve's third equation, relation to PV 505—506
Painleve's third equation, simplified forms of 502 503
Painleve's third equation, solutions to, rational in  503
Painleve's third equation, systems equivalent to 504 505
Parabolic PDE 2
Parametric relations between solutions of PIII 448—449
Parametric relations between solutions of PIV 449—450
Parametric relations between solutions of PV 450
Parametric relations between solutions of PVI 450—452
Phase line, singular points on 248
Phase plane, singular points in 250
Phase space 3
Phase space, dimensional analysis 330
Piston problem, general plane 537
Piston problem, spherical and cylindrical, for a converging shock 529
Plasma physics, a 3-dimensional model from 361 364
Plasma physics, a DE arising in 240
Plasma physics, connection problem in 240
Plasma physics, solution of a connection problem in 240—244
Poisson — Boltzmann equation 60
Porous media equation 223
Porous media equation, BVP for 224
Porous media equation, existence of solutions for BVP for 224—230
Porous media equation, similarity forms of 223
Porous media equation, weak solution for 224
psi series 359
Psi series, solution of nonlinear DE 96
Quadratic systems, homogenous 286
Quadratic systems, normal form of 285
Quartic lattice system, free end Toda lattice 411—413
Quartic lattice system, integrability of 409—411
Radius of convergence of series 127
Radius of convergence of series, computation of 127—130
Radius of convergence of series, theorems for 128
Rational solutions of PII 447
Regular singular point 72
Relation of PII to itself 446—447
Relation of PII to PXXXIV 445
Repellor 354
Resonances in power series expansions 141
Riccati equation 28 83 85
Riccati equation and PV 497
Riccati equation, linearization of 28—29
Rikitake two-disk system, Painleve property of 360 362—364
Scale invariance 24
Second order nonlinear DE, relation to second order linear DE 37
Second order nonlinear DE, relation to third order linear DE 33
Series solution for nonlinear DE 97
Series solution, computational aspects of 97
Series solution, radius of convergence of 97
Shallow water equations, dam break initial conditions for 539—540
Shallow water equations, gravity currents releases and 538
Shock wave, converging 529
Similarity solutions as intermediate asymptoties 512
Simple pendulum, nonharmonic nonlinear oscillator 100—102
Simple pendulum, series solution of IVP for 103—108
Sine — Gordon equation and PII 428—429
Singular points at infinity for a two dimensional linear system 268—273
Singular points of second order linear DE 9
Singularities of nonlinear DE 79
Singularities of nonlinear DE, essential singularities 82
Singularities of nonlinear DE, isolated singularities 82
Singularities of nonlinear DE, logarithmic branch points 81
Singularities of nonlinear DE, poles 82
Singularities, essential 423
Singularities, fixed 421
Singularities, movable 422
Special elementary solutions of PIII 436—437
Special elementary solutions of PVI 438—442
Spherical cavity, collapse of-in a perfect gas 520
Spherical cavity, global solutions for 521—529
Stability analysis of similarity solutions for arbitrary current releases 544
Symmetries of DE 24
Third order linear DE relation to second order nonlinear DE 33
Thomas — Fermi equation 54
Thomas — Fermi equation, asymptotic solutions of 164
Thomas — Fermi equation, BVP for 168 218
Thomas — Fermi equation, embedding of asymptotic solutions for 172 174
Thomas — Fermi equation, IVP using majorants 115
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