Файл	Ном	Сабт карда шуд
Nabieva Manzura	INVARIANTS OF THE GROUP OF TRANSFORMATIONS OF THE PLANE AND THEIR USE	37

Authors:  Nabieva Manzura – Teacher of the Department of Mathematical Analysis named after professor A.Mukhsinov State Educational Instituon “KhSU named after academician B. Gafurov” (Tajikistan Republic, Khujand)

JOURNAL NUMBER: 2(57). YEAR OF ISSUE: 2021. LANGUAGE OF THE ARTICLE: Russian

ANNOTATION

This article is devoted to the basic concept and properties of one – parameter groups and their invariants. Since a necessary and sufficient condition for invariance is the solution of a linear partial differential equation of the first order, the invariants of several frequently occurring groups are determined using the characteristic equation. Invariants of one – parameter groups are applied to the integration of nonlinear ordinary differential equations of the first order. Note that the results obtained by the methods of group analysis in the above discussed examples cannot be obtained by conventional methods.

KEY WORDS

plane, one – parameter group, infinitesimal operator, group operator differential equation, change of variables, invariant.

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