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Symmetries of Integro-Differential Equations: With Applications in Mechanics and Plasma Physics /
http://lt-jds.jinr.ru/record/60916
This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries. Differential and integro-differential equations, especially nonlinear, present the most effective way for describing complex processes. Therefore, methods to obtain exact solutions of differential equations play an important role in physics, applied mathematics and mechanics. This book provides an easy to follow, but comprehensive, description of the application of group analysis to integro-differential equations. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. It introduces new applications and extensions of the group analysis method. The authors have designed a flexible text for postgraduate courses spanning a variety of topics.Ibragimov, Nail H.Mon, 22 Jul 2013 11:19:35 GMThttp://lt-jds.jinr.ru/record/60916urn:ISBN:9789048137978Springer Netherlands,2010.Bogolyubov renormalization group and symmetry of solution in mathematical physics
http://lt-jds.jinr.ru/record/23162
Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparameterisation one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of new approach to solution for a problem of self-focusing laser beam in a non-linear medium.Shirkov, Dmitrij V.Thu, 28 Oct 2010 07:47:36 GMThttp://lt-jds.jinr.ru/record/23162Functional selfsimilarity and renormalization group symmetry in mathematical physics
http://lt-jds.jinr.ru/record/22944
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the regular algorithm for finding renormalization group-type symmetries using the contemporary theory of Lie groups of transformations.Kovalev, Vladimir F.Thu, 28 Oct 2010 07:47:18 GMThttp://lt-jds.jinr.ru/record/22944The Bogoliubov renormalization group and solution symmetry in mathematical physics
http://lt-jds.jinr.ru/record/1512
Shirkov, Dmitrij V.Mon, 27 Sep 2010 20:18:47 GMThttp://lt-jds.jinr.ru/record/1512urn:ISSN:0370-15732001Group analysis and renormgroup symmetries
http://lt-jds.jinr.ru/record/1303
Kovalev, Vladimir F.Mon, 27 Sep 2010 20:02:29 GMThttp://lt-jds.jinr.ru/record/1303urn:ISSN:0022-24881998The renormalization group symmetry for solution of integral equationsSymmetry in nonlinear mathematical physics. Part 1, 2, 3
http://lt-jds.jinr.ru/record/298
Kovalev, Vladimir F.Fri, 24 Sep 2010 20:27:59 GMThttp://lt-jds.jinr.ru/record/298Nats\=\i onal. Akad. Nauk Ukra\"\i ni \=Inst. Mat.2004