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Applications of Group-Theoretical Methods in Hydrodynamics by V.K. Andreev, O.V. Kaptsov, Vladislav V. Pukhnachev, A.A.

By V.K. Andreev, O.V. Kaptsov, Vladislav V. Pukhnachev, A.A. Rodionov

It was once in the past that team research of differential equations grew to become a robust instrument for learning nonlinear equations and boundary worth difficulties. This research used to be specially fruitful in software to the elemental equations of mechanics and physics as the invariance rules are already taken with their derivation. it really is not at all a accident that the equations of hydrodynamics served because the first item for using the hot principles and techniques of workforce research which have been built by way of 1. V. Ovsyannikov and his institution. The authors rank themselves as disciples of the college. the current monograph bargains normally with group-theoretic class of the equations of hydrodynamics within the presence of planar and rotational symmetry and in addition with building of actual suggestions and their actual interpretation. it really is worthy noting that the idea that of actual strategy to a differential equation isn't really outlined conscientiously; various authors are aware of it in numerous methods. the concept that of tangible resolution expands in addition to the development of arithmetic (solu­ tions in basic features, in quadratures, and in distinct services; options within the kind of convergent sequence with successfully computable phrases; strategies whose looking reduces to integrating usual differential equations; and so on. ). We examine it justifiable to complement the set of tangible recommendations with rank one and rank in­ variation and in part invariant strategies to the equations of hydrodynamics.

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Greek not only is spoken by members of the Greek minority in southern Albania but also is understood by many Albanians near the Greek border. Most Kosovo Albanians speak and understand Serbo-Croatian. 14 ALBANIA about the Albanian people as they are known today. In his History written in 1079–1080, the Byzantine historian Michael Attaleiates was the first to refer to the Albanoi as having taken part in a revolt against Constantinople in 1043 and to the Arbanitai as subjects of the duke of Dyrrachium.

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