Meleshko S.V. — Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering :: Электронная библиотека попечительского совета мехмата МГУ

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Meleshko S.V. — Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering

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Название: Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering

Автор: Meleshko S.V.

Аннотация:

Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 352

Добавлена в каталог: 13.12.2009

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Предметный указатель

Admitted Lie group      173
Autonomous system      44
Baecklund theorem      228
Baecklund transformation      21
Bernoulli integral      72
Boltzmann equation      252
Boussinesq equation      235
Breaking time      9
Burgers equation      21
Cartan character      129
Cartan number      129
Cartan theorem      130
Cartan — Khaeler theorem      130
Cauchy method      5
Characteristic curve      5 137 139
Characteristic equation      45
Characteristic matrix      44
Characteristic surface      45
Characteristic system      5
Characteristic vector      44
Commutator      177
Complete integral      9 12
Complete system      15
Completely integrable system      11 61
Contact transformation      18
Darboux equation      20
Defect of a partially invariant solution      205
Dimension of physical quantity      53
Double wave      74
Double wave in rigid plastic body      111
Envelope      9
Equivalence Lie group      188
Equivalence with respect to the function      22
Equivalent transformation      186
Erugin method      33
Functionally invariant solution      31
Generalized functionally invariant solution      35
Generalized Riemann invariant      69
Generalized simple wave      141
Group classification      186
Hodograph method      48
Homogeneous system      44
Hopf — Cole transformation      21
Hyperbolic system      45
Inner automorphism      183
Intensive explosion      56
Intermediate integral      37
Invariant manifold      172
Invariant of a Lie group      171
Invariant of a scale group      51
Invariant solution      194
Involutive symbol      130

Involutive system      130
Klein — Gordon equation      26
Korteweg — de Vries equation      28
Laplace invariants      22
Laplace transformation      24
Legendre transformation      19
Lie algebra      178
Lie group of transformations      165 193
Lie theorem      167
Lie — Baecklund group of transformations      156
Lie — Baecklund operator      233
Linear equation      2
Linear hyperbolic equation      22
Linear profile of velocity      58
Method of differential constraints      131
Monge — Ampere equation      40 230
Multiple travelling wave      59
Navier — Stokes equations      208
Optimal system of subalgebras      183
Order of equation      2
Overdetermined system      44
Ovsiannikov theorem      74
Partially invariant solution      205
Point transformation      18
Poisson bracket      14
Prandtl — Reuss equations      105
Prolonged generator      168
Quasilinear equation      2
Quasiregular coordinate system      130
Rank of a partially invariant solution      205
Rarefaction wave      145
Regularly assigned manifold      171
Riemann invariant      47
Riemann wave      47
Scale group      50
Self—similar solution      26 54
Separation of variables      25
Shock wave structure      28
Similar subalgebra      180
Simple integral element      68
Simple wave      69
Singular integral      10
Smirnov — Sobolev formula      33
Solitary wave      29
Subalgebra of a Lie algebra      180
Symbol $G_{q}$       129
System of quasilinear differential equations      44
Tangent conditions      224
Tangent transformation      18 224
Travelling wave      27 59
Triple wave      121
Vlasov equation      250
Wave parameter      66

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