Sophus Lie and harmony in mathematical physics, on the 150th anniversary of his birth. Translated and annotated by O. Kowalski. (Czech) Zbl 0830.01013

Ibragimov, Nail H.

Pokroky Mat. Fyz. Astron. 39, No. 4, 192-208 (1994).

This article is the Czech translation of the paper published in Math. Intell. 16, No. 1, 20–28 (1994; Zbl 0795.01008).
First, the author gives a short biography of S. Lie. Next, he presents the classification of some differential equations of the second order with respect to Lie groups and Lie’s algorithm of the integration of these equations. Later, he deals with the reduction of differential equations to the linear form and the so-called “invariant solutions”. Then a group approach to Riemann’s method of integration of a partial differential equation is given. Finally, the principle of the invariance in connection with the Laplace equation, the heat conductivity equation, the wave equation and Kepler rules are considered.

Reviewer: Przemysław Skibiński (Łódź)

MSC:

01A55	History of mathematics in the 19th century
01A60	History of mathematics in the 20th century
34-03	History of ordinary differential equations
22-03	History of topological groups
35-03	History of partial differential equations
58-03	History of global analysis

Keywords:

short biography; Lie algebras; differential equations

Citations:

Zbl 0795.01008