文档介绍：arXiv: v2 21 Dec 1998
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NEUTOSO AHMTCLPHYSICS MATHEMATICAL OF EQUATIONS IN
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Contents
Introduction 4
1. Differential calculus mutative algebras 6
. Linear differential operators 6
. Multiderivations and the Diff-plex 8
. Jets 11
. plex 13
. Differential forms and the de plex 13
. Left and right differential modules 16
. The Spencer cohomology 19
. Geometrical modules 25
2. Algebraic model for Lagrangian formalism 27
. Adjoint operators 27
. Berezinian and integration 28
. Green’s formula 30
. The Euler operator 32
. Conservation laws 34
3. Jets and nonlinear differential equations. Symmetries 35
. Finite jets 35
. Nonlinear differential operators 37
. Infinite jets 39
. Nonlinear equations and their solutions 42
. Cartan distribution on J k(π) 44
. Classical symmetries 49
. Prolongations of differential equations 53
. Basic structures on infinite prolongations 55
. Higher symmetries 62
4. Coverings and nonlocal symmetries 69
. Coverings 69
. Nonlocal symmetries and shadows 72
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