Lie group analysis. Classical heritage

Front cover......Page 1
Preface......Page 4
Contents......Page 5
Sophus Lie. General theory of partial differential equations of an arbitrary order......Page 8
1 Comparative review of new studies on diffrential equations......Page 11
2 Addition to the Monge's theory of characteristics......Page 23
3 Every infinitesimal contact transformation of a partial differential equation generates a special integral manifold......Page 39
4 Partial diааerential equations admitting an infinite group......Page 57
Editor's notes......Page 70
Sophus Lie. Integration of a class of linear
partial differential equations by means of
definite integrals......Page 72
First Part: Transformation theory for linear second-order
partial differential equations......Page 76
Second Part: Integration of linear partial differential
equations admitting infinitesimal transformations......Page 98
Review by the author......Page 107
Editor's notes......Page 109
1. Geometric proof of nonexistence of proper osculating transformations of plain curves......Page 110
2. Analytical proof of the same theorem......Page 113
3. Single-valued transformations of plane curves......Page 119
4. Transformations of n-dimensional manifolds M_n in an n + 1 -dimensional space......Page 121
6. A class of multivalued transformations of three-dimensional spaces......Page 124
Editor's Notes......Page 128
L.V. Ovsyannikov. Group properties of the Chaplygin equation......Page 130
1. The Chaplygin equation and the Chaplygin function......Page 132
2. The Laplace invariants......Page 134
3. Calculation of the group for the second-order equation......Page 138
4. Determination of the admissible Chaplygin functions......Page 143
5. Canonical forms of the admissible Chaplygin equation......Page 150
6. The Tricomi type equations......Page 153
7. The Laplace type equations......Page 156
Editor's Notes......Page 161
Bibliography......Page 162
Back cover......Page 165