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Sachdev P.L. Ч Nonlinear ordinary differential equations and their applications
Sachdev P.L. Ч Nonlinear ordinary differential equations and their applications

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Ќазвание: Nonlinear ordinary differential equations and their applications

јвтор: Sachdev P.L.

јннотаци€:

Presents simple analytic methods which are readily accessible for use in applications. These include transformations, phase plane analysis, integral equation formulation, shooting arguments, local and asymptotic analysis, singular point analysis, and others. The applications, reflecting the research.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1990

 оличество страниц: 606

ƒобавлена в каталог: 17.02.2014

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
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      122Ч127
Asymptotic solutions of cylindrical and spherical Burgers equation      516Ч519
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      217Ч218
Blasius equation, series solution with IC at infinity      99Ч100
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      552Ч558
Bore over a sloping beach approximate treatment of, nonexistence of a self-similar solution      549Ч551
Bore over a sloping beach approximate treatment of, numerical solution for      549
Boundary layer equations, asymptotic series solution of BVP for      122Ч127
Boundary layer theory, BVP for      118
Boundary layer theory, BVP over an infinite domain      117Ч121
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 215Ч216
Boussinesq equation      427 428 431 434
Briot Ч Bouquet equation      88
Briot Ч Bouquet equation, equations reducible to      90Ч92
Briot Ч Bouquet equation, psi series solutions of      96
Briot Ч Bouquet equation, series solutions of      93Ч96
Briot Ч Bouquet equation, simple cases of      88Ч90
Briot Ч Bouquet equation, singularities of      88
Briot Ч Bouquet system and Pv      494Ч495
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      320Ч324
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      539Ч540
Deformation of a circular membrane BVP for      243Ч244
Degree of DE      3
Dirichlet series for BVP in boundary layer theory      118Ч121
Dominant behaviour of DE      140
Electromagnetic Theory, a DE arising in      231
Electromagnetic Theory, solutions of a BVP relating to      231Ч239
Elliptic PDE      2
Embedding of asymptotic solutions      164
Emden equation-phase plane analysis of      301
Emden Ч Lane Ч Fowler equation      54 60 61
Equidimensionality      24
Essential singularities      423
Euler Ч Painleve transcendents      187
Euler Ч Painleve transcendents, connection problems for      130 137
Euler Ч Painleve transcendents, Kamke's collection and      201Ч208
Euler Ч Painleve transcendents, Murphy's collection and      208Ч211
Euler Ч Painleve transcendents, other DE related to      200
Euler Ч Painleve transcendents, relation to GBE with damping      187Ч188
Euler Ч Painleve transcendents, series solution for      189 196
Euler Ч 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      135Ч138
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      516Ч519
Generalized Duffing equation      55
Gravity current releases, global solutions for      542Ч545
Gravity current releases, global solutions for, self-similar solutions for      541
Green's function for linear BVP      16Ч21
Hamiltonian systems, free end Toda lattice      411Ч413
Hamiltonian systems, Henon Ч Heiles      394Ч409
Hamiltonian systems, quartic lattice      409Ч411
Henon Ч Heiles system, integrability of and chaos in      394Ч409
Henon Ч Heiles system, Painleve analysis for      394Ч403
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      419Ч420
Integrability of a quadratic third order DE      420
Integrability of DE      357Ч358
Integral equation formulation of BVP      175
Internal gravity waves      324
Inverse scattering transform      138
Irrational right hand sides, second order nonlinear DE with      452Ч454
Irrational right hand sides, singular solutions of DE with      453Ч454
Irregular singular point      74
Isothermal atmosphere, nonlinear periodic solutions and      326Ч327
Isothermal atmosphere, nonlinear travelling waves and      324
Iteration for nonlinear BVP      175
Iterative solutions for IVP      151Ч153
K-dV equation and PI      429 431
Kuramoto model-steady-singularities of and chaos in      413Ч418
Laminar boundary layer, BVP for      244
Laminar convection over a linear heat source, solution of BVP for      106
Langmuir Ч Blodgett equation      55
Langmuir Ч Boguslavski equation      55
Langmuir's equation      62
Laurent series      140
Levinson's method      154Ч158
Lindeloeff's majorant      112Ч116
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      131Ч132
Local analysis of DE - method of Painleve      132
Lorenz system, integrability of and chaos in      365Ч394
Lorenz system, integrable cases of      375Ч377
Lorenz system, numerical solutions of and singularities in      386Ч394
Lorenz system, Painleve analysis of      378Ч382
Lorenz system, perturbation analysis for periodic solutions of      368Ч374
Lotke Ч Volterra model, Painleve property of      361 364
Majorants      108
Majorants for first order DE      109Ч110
Majorants, Cauchy      111
Majorants, Lindeloeff      112Ч114
Malmquist theorem      96
Modified Koreteweg Ч 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      178Ч180
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      309Ч314
Nonlinear PDE - solutions of - as infinite series      512
Nonlinear Schroedinger equation and Painleve equation      431
Nonsimple singular points for two-dimensional systems      273Ч284
Normal quadratic systems, applications of      287
Normal quadratic systems, classification of singular points for      292Ч301
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 Ч Bouquet system and      494Ч495
Painleve's fifth equation, degenerate cases of      501
Painleve's fifth equation, radial wave equation and      497
Painleve's fifth equation, rational solutions of      499Ч501
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      495Ч496
Painleve's first equation      460
Painleve's first equation and beyond      472
Painleve's first equation, asymptotic behavior for      468Ч469 466Ч467
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      470Ч472
Painleve's first equation, shooting techniques for      472
Painleve's first equation, solution as quotient of integral functions      471Ч472
Painleve's first equation, solution with movable poles      461Ч468
Painleve's fourth equation      482
Painleve's fourth equation, Hermite equation and      492
Painleve's fourth equation, rational solutions of      489 490Ч493
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      483Ч486 489Ч490
Painleve's property      138Ч139
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      475Ч478
Painleve's second equation, numerical study of      475 478Ч482
Painleve's second equation, relation to K-dV equation      474Ч475
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      184Ч185
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 85Ч86
Painleve's third equation      501
Painleve's third equation, asymptotic representation of solutions of      508Ч510
Painleve's third equation, expansions of solutions about zero      506Ч507
Painleve's third equation, perturbation solutions about unity      507
Painleve's third equation, relation to PV      505Ч506
Painleve's third equation, simplified forms of      502 503
Painleve's third equation, solutions to, rational in $z^{113}$      503
Painleve's third equation, systems equivalent to      504 505
Parabolic PDE      2
Parametric relations between solutions of PIII      448Ч449
Parametric relations between solutions of PIV      449Ч450
Parametric relations between solutions of PV      450
Parametric relations between solutions of PVI      450Ч452
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      240Ч244
Poisson Ч Boltzmann equation      60
Porous media equation      223
Porous media equation, BVP for      224
Porous media equation, existence of solutions for BVP for      224Ч230
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      411Ч413
Quartic lattice system, integrability of      409Ч411
Radius of convergence of series      127
Radius of convergence of series, computation of      127Ч130
Radius of convergence of series, theorems for      128
Rational solutions of PII      447
Regular singular point      72
Relation of PII to itself      446Ч447
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      28Ч29
Rikitake two-disk system, Painleve property of      360 362Ч364
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      539Ч540
Shallow water equations, gravity currents releases and      538
Shock wave, converging      529
Similarity solutions as intermediate asymptoties      512
Simple pendulum, nonharmonic nonlinear oscillator      100Ч102
Simple pendulum, series solution of IVP for      103Ч108
Sine Ч Gordon equation and PII      428Ч429
Singular points at infinity for a two dimensional linear system      268Ч273
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      436Ч437
Special elementary solutions of PVI      438Ч442
Spherical cavity, collapse of-in a perfect gas      520
Spherical cavity, global solutions for      521Ч529
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 Ч Fermi equation      54
Thomas Ч Fermi equation, asymptotic solutions of      164
Thomas Ч Fermi equation, BVP for      168 218
Thomas Ч Fermi equation, embedding of asymptotic solutions for      172 174
Thomas Ч Fermi equation, IVP using majorants      115
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