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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Applications of Group-Theoretical Methods in Hydrodynamics (Paperback, Softcover reprint of hardcover 1st ed. 1998)
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Applications of Group-Theoretical Methods in Hydrodynamics (Paperback, Softcover reprint of hardcover 1st ed. 1998)
Series: Mathematics and Its Applications, 450
Expected to ship within 10 - 15 working days
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It was long ago that group analysis of differential equations
became a powerful tool for studying nonlinear equations and
boundary value problems. This analysis was especially fruitful in
application to the basic equations of mechanics and physics because
the invariance principles are already involved in their derivation.
It is in no way a coincidence that the equations of hydrodynamics
served as the first object for applying the new ideas and methods
of group analysis which were developed by 1. V. Ovsyannikov and his
school. The authors rank themselves as disciples of the school. The
present monograph deals mainly with group-theoretic classification
of the equations of hydrodynamics in the presence of planar and
rotational symmetry and also with construction of exact solutions
and their physical interpretation. It is worth noting that the
concept of exact solution to a differential equation is not defined
rigorously; different authors understand it in different ways. The
concept of exact solution expands along with the progress of
mathematics (solu tions in elementary functions, in quadratures,
and in special functions; solutions in the form of convergent
series with effectively computable terms; solutions whose searching
reduces to integrating ordinary differential equations; etc. ). We
consider it justifiable to enrich the set of exact solutions with
rank one and rank two in variant and partially invariant solutions
to the equations of hydrodynamics."
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