Approximate symmetries. (English. Russian original) Zbl 0683.35004

Baĭkov, V. A.; Gazizov, R. K.; Ibragimov, N. H.

Math. USSR, Sb. 64, No. 2, 427-441 (1989); translation from Mat. Sb., Nov. Ser. 136(178), No. 4(8), 435-450 (1988).

The methods of classical group analysis admit to select among all equations of mathematical physics equation remarkable for their properties of symmetry. Unfortunately, any small perturbation of an equation distroys an admissible group. This reduces the applied value of these equations and the methods of group theory in general. Hence it is necessary to develop methods of group analysis which are stable under small perturbations of differential equations. The aim of this paper is to develop such method based on the concepts of an approximate group of transforms and of approximate symmetries.

Reviewer: J.Tian

MSC:

35A30	Geometric theory, characteristics, transformations in context of PDEs
35G05	Linear higher-order PDEs

Keywords:

stability; perturbation