Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Formal Operators Operators Admitted by Generalized Differential Equations and Principle of Factorization

Author(s):

L. V. Linchuk

Russian State Pedagogical University
Saint-Petersburg
Russia

lidiya@p110.f289.n5030.z2.fidonet.org

Abstract:

Last researches have shown that we can considerably expand classes of symmetries investigated in group analysis using formal approach. In this paper the main ideas of theory of formal operators are spread on the space of three variables x, y, w, and then we proved the fundamental principle of symmetry analysis of the generalized differential equations y⁽ⁿ⁾=F(x,y,w,...,w^(n-1), y^(n-1),w⁽ⁿ⁾) – principle of factorization. In particular, this class includes functional differential equations, therefore the approach can be applied for search of factor system and precise solutions of these equations. The main part of the paper is devoted to research of base of invariant space of admitted operator and algorithms of its search, as these ideas allow to spread principle of factorizations on the class of generalized differential equations. We considered the most perspective classes of operators defining the given type of factorization.

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