Symmetries and Conservation Laws for Differential Equations of Mathematical Physics

Front Cover
American Mathematical Soc.
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Contents

Ordinary Differential Equations
1
2 Ordinary differential equations of arbitrary order
6
3 Symmetries of distributions
10
4 Some applications of symmetry theory to integration of distributions
17
5 Generating functions
29
an example of using symmetries
33
FirstOrder Equations
37
2 Infinitesimal contact transformations and characteristic fields
50
2 The Cartan distribution on J𝛑 and its infinitesimal automorphisms
138
3 infinitelyprolonged equations and the theory of higher symmetries
154
4 Examples of computation
164
Conservation Laws
185
2 The Cspectral sequence
187
3 Computation of conservation laws
206
4 Symmetries and conservation laws
214
Nonlocal Symmetries
221

3 Complete integrals of firstorder differential equations
60
The Theory of Classical Symmetries
69
2 Jet manifolds and the Cartan distribution
72
3 Lie transformations
83
4 Classical symmetries of equations
92
5 Examples of computations
96
6 Factorization of equations by symmetries
108
7 Extrinsic and intrinsic symmetries
116
Higher Symmetries
123
coverings
238
3 Nonlocal symmetries
249
nonlocal symmetries of the Burgers equation
251
5 The problem of symmetry reconstruction
257
6 Symmetries of integrodifferential equations
266
From Symmetries of Partial Differential Equations Towards Secondary Quantized Calculus
301
Bibliography
323
Index
329
Copyright

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