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Qualitative Methods of Studying Models of Mathematical Physics

Work number - P 38 AWARDED

Authors: Kochubei A.N., Rebenko O.L., Mykytiuk I.V., Prykarpatsky A.K., Samoilenko V.H., Feldman G.M., Shcherbyna M.V.

Submitted by the Institute of Mathematics of the National Academy of Sciences of Ukraine.


The cycle of scientific works consists of 16 monographs and 122 scientific articles published during the period from 1975 to 2016.

The cycle is devoted to the studying actual problems of the theory of dynamic systems of modern mathematical and theoretical physics as well as the construction of new effective methods for qualitative analysis of a wide class of models of mathematical physics and their applications. In the works of the cycle, considerable attention is paid to the study of a wide range of mathematical models that are used in physics, mechanics, the theory of random graphs, quantum informatics, the theory of information transmission, and other branches of natural science.

Integrable systems, partial differential equations and fractional-differential equations describing non-classical diffusion (anomalously slow diffusion on fractals), methods of p-adic analysis, etc. are considered. In this case, mathematical objects of physical origin are studied by methods of various branches of mathematics, from functional analysis to algebraic geometry and the theory of Lie groups.

The following topical fields of modern mathematical physics, such as methods of non-archimedian analysis and non-archimedian stochastics, qualitative-analytic analysis of integrability of nonlinear dynamic systems of mathematical physics, qualitative-analytical methods of infinite-dimensional analysis of quantum field theory and statistical mechanics, probabilistic methods in the problems of spectral theory and in groups are developed and their application in the study of various models of mathematical and theoretical physics are given. The Dyson hypothesis is proved.

Number of publications: 16 monographs, 122 articles. The total number of references to authors' publications is 1945, h-index=12 (according to SCOPUS) and 7352, h-index = 23 (according to Google Scholar Citation). On this subject, 15 doctoral and 37 candidate's theses are defended.