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Lectures on the Theory of Group Properties of Differential Equations
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When I studied at Novosibirsk State University (Russian) I was lucky to have such brilliant teachers in mathematics as M.A. Lavrentyev, S.L. Sobolev, A.I. Mal’tsev, Yu.G. Reshetnyak and others. But it were L.V. Ovsyannikov’s lectures in Ordinary differential equations, Partial differential equations, Gas dynamics and Group properties of differential equations that were of the most benefit for me. I attended his course “Group properties of differential equations” when I was a third-year student. His lectures provided a clear introduction to Lie group methods for determining symmetries of differential equations and a variety of their applications in gas dynamics and other nonlinear models as well as Ovsyannikov’s remarkable contribution to this classical subject. His lectures were spectacular not only due to the brilliant presentation of the material but also due to absolutely new discoveries for us. I remember one of our most emotional student’s repeated exclamations like “Wonderful, . . . Incredible!” every time when Ovsyannikov revealed most unusual properties of symmetries or unexpected methods.
His lecture notes of this course were published in 1966 with the print of 300 copies only. Since then the Notes were neither reprinted nor translated into English, though they contain the material that is useful for students and teachers but cannot be found in modern texts. For example, theory of partially invariant solutions developed by Ovsyannikov and presented in x3.5, x3.6 is useful for investigating mathematical models described by systems of nonlinear differential equations. It is important to make this classical text available to everyone interested in modern group analysis.
In order to adapt the text for modern students I made several minor changes in the English translation. In particular, sections have been divided into subsections and few misprints have been corrected. Part of the problems formulated in x3.7 have been completely or partially solved since 1966. But we did not make any comments on this matter in the present translation.
N.H. Ibragimov - Personal Name
1st Edtion
918 1 04 036944 1
NONE
Lectures on the Theory of Group Properties of Differential Equations
Economics
English
Highcr Edalion Limited Company
2013
China
1-154
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