Read e-book online Applications of Group-Theoretical Methods in Hydrodynamics PDF

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

It used to be in the past that workforce research of differential equations grew to become a strong device for learning nonlinear equations and boundary price difficulties. This research used to be specifically fruitful in program to the fundamental equations of mechanics and physics as the invariance ideas are already fascinated with their derivation. it really is not at all a twist of fate that the equations of hydrodynamics served because the first item for utilizing the hot rules and techniques of workforce research that have been constructed through 1. V. Ovsyannikov and his college. The authors rank themselves as disciples of the varsity. the current monograph offers regularly with group-theoretic class of the equations of hydrodynamics within the presence of planar and rotational symmetry and likewise with development of tangible recommendations and their actual interpretation. it truly is worthy noting that the idea that of tangible option to a differential equation isn't outlined carefully; diverse authors know it in numerous methods. the concept that of actual answer expands in addition to the growth of arithmetic (solu­ tions in simple capabilities, in quadratures, and in certain capabilities; suggestions within the kind of convergent sequence with successfully computable phrases; options whose looking out reduces to integrating traditional differential equations; and so forth. ). We reflect on it justifiable to complement the set of actual ideas with rank one and rank in­ variation and in part invariant suggestions to the equations of hydrodynamics.

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Applications of Group-Theoretical Methods in Hydrodynamics (Mathematics and Its Applications) by V.K. Andreev,O.V. Kaptsov,Vladislav V. Pukhnachev,A.A. Rodionov

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