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Information × Registration Number 0225U002125, (0120U100173) , R & D reports Title Symmetry and integrability of equations of modern mathematical physics popup.stage_title Симетрія та інтегровність рівнянь сучасної математичної фізики Head Nikitin Anatolii H., Доктор фізико-математичних наук Registration Date 19-02-2025 Organization Institute of Mathematics of the National Academy of Sciences of Ukraine popup.description1 The aim of the project is to create and substantiate new methods for the study of different types of symmetries of equations of modern mathematical physics, their application for the construction and analysis of models with physically motivated symmetry groups, as well as finding exact solutions of some actual models of mathematical physics. popup.description2 Research report: 322 p., 21 chapters, 13 tables, 15 figures, 106 sources. Keywords: SYMMETRY, INTEGRATION, EXACT SOLUTIONS, NONLINEAR MODELS, LIE ALGEBRAS AND LIE GROUPS. The object of the research is nonlinear models of mathematical physics. The aim of the project is to create and substantiate new methods for the study of different types of symmetries of equations of modern mathematical physics, their application for the construction and analysis of models with physically motivated symmetry groups, as well as finding exact solutions of some actual models of mathematical physics. Research methods are modern methods of mathematical physics and group analysis of differential equations, theory of Lie algebras and Lie groups. The report contains the main results of the research and a list of scientific works published within the framework of this research. As a result of the research, new methods for studying various types of symmetries of equations of modern mathematical physics were created and substantiated, their application for constructing and analyzing models with physically motivated symmetry groups was investigated, group classification was performed and exact solutions of some actual models of mathematical and theoretical physics, mathematical biology were constructed. The obtained theoretical results were used in problems of mathematical modeling, meteorology, problems of information encryption, spread and forecasting of infectious diseases, problems of pattern recognition, in the study of dynamic conflict systems, etc. Product Description popup.authors Yehorchenko Iryna A. Antoshyna Kateryna O. Boiko Viacheslav M. Vinnichenko Oleksandra O. Vanieieva Olena O. Voloshyn Oleksandr A. Davydovych Vasyl V. Zhalii Oleksandr Yu. Zorii Nataliia V. Karataieva Tetiana V. Koval Serhii D. Koshmanenko Volodymyr D. Lokaziuk Oleksandra V. Mochuk Olena V. Nikitin Anatolii H. Nesterenko Maryna O. Popovych Dmytro R. Popovych Roman O. Posenko Halyna B. Rebenko Oleksii L. Samoilenko Valerii H. Satur Oksana R. Skrypnyk Volodymyr I. Spichak Stanislav V. Staryi Mykola S. fon Dichter Elina Ye. Chapovskyi Yevhenii Y. Cherniha Roman M. popup.nrat_date 2025-02-19 Close