Analytical Methods in Differential Equations

The book compiles papers presented at the International Conference 'Advances in Applications of Analytical Methods in Solving Differential Equations', held in honour of Academician Lev V. Ovsiannikov’s 105th birthday anniversary. This collection reflects his extensive contributions to the theory of differential equations, modelling, and the application of analytical methods. In addition to classical methods such as analytical integration of systems of equations and their applications in various fields of Science and Engineering, the book explores new areas of research. This includes the application of group analysis to novel mathematical models and nonlinear problems, particularly equations with nonlocal terms (symmetries of difference and differential equations, as well as fractional differential equations). One of the notable contributions in the book is the development of a Hamiltonian approach for delay differential equations, representing a novel area of research that has not been previously explored. The book is anticipated to appeal to a broad audience of experts in applied mathematics, fluid dynamics, and modelling, as well as to young scientists and graduate students interested in the analysis of nonlinear equations.

• Lie group analysis of local and nonlocal differential equations;
• Mathematical modelling for fluid dynamics;
• Hamiltonian approach to delay ODEs

Sergey V. Meleshko received his M.Sc. from Novosibirsk State University and his Ph.D. from the Institute of Hydrodynamics (Novosibirsk) in 1981 under the guidance of Academician Nikolay N. Yanenko and Prof. Vasiliy P. Shapeev. In 1991 he defended the doctor degree "Classification of solutions with degenerate hodograph of the gas dynamics and plasticity equations" in the Institute of Mathematics and Mechanics (Sverdlovsk, now Ekaterinburg). Beginning in 1979, he worked as a researcher, senior researcher and leading researcher at the Institute of Theoretical and Applied Mechanics in Novosibirsk. At the same time, he was a professor at Novosibirsk State University, where from July 1991 onwards he served as deputy dean. In 1996 he moved to work at Suranaree University of Technology, where he guided more than 20 students towards their PhD degrees. The main research interests of S.V. Meleshko include analytical methods for constructing exact solutions of partial differential equations (in particular, the method of differential constraints and group analysis of differential equations); symbolic (analytical) calculations on a computer; and mathematical and numerical modeling. He is co-author of more than 240 scientific papers. Among his publications are the following books: S.V. Meleshko `Methods for constructing exact solutions', 2010, Springer; Yu.N.Grigoriev, N.H.Ibragimov, V.F. Kovalev, S.V.Meleshko `Symmetries of integro-differential equations and their applications in mechanics and plasma physics', 2010, Springer; Yu.N.Grigoriev, V.F. Kovalev, S.V.Meleshko `Symmetries of nonlocal equations: theory and applications', 2018, Nauka (in Russian).

More recently (2019, 2021, 2022, 2024) he has been among the organizers of several international conferences. Following the conferences, he was the leader of the editorial teams of the published Proceedings of the papers presented at the conferences.

Eckart Schulz obtained his Ph.D. in Operator Algebras from the University of Saskatchewan in 1991 and joined the School of Mathematics at Suranaree University of Technology as regular faculty shortly afterwards. Since then he has guided more than 10 students to their Master’s and Ph.D. degrees. His research interests and publications include harmonic analysis, continuous and discrete wavelets, as well as group analysis of stochastic differential equations. He has held the position of Department Head, and has been deeply involved in organizing six international conferences in recent years, which included editing the respective conference proceedings.

Dr. Sibusiso Moyo is a researcher with expertise in differential equations and their applications. Most of her work has been dedicated to the analysis of differential equations using group theoretic methods, numerical analysis and applications in different branches of science like mathematical physics and engineering. She graduated with a PhD in Mathematics from the University of Natal (now UKZN) in 2002. Her current position is that of Deputy Vice-Chancellor (DVC) Research, Innovation and Postgraduate Studies at Stellenbosch University from 1^st September 2022. She has published widely on differential equations and their applications. Apart from the PhD she holds a Master’s degree in Tertiary Education Management (with distinction) from the University of Melbourne, Australia.　Her previous positions at Durban University of Technology in South Africa include DVC Research, Innovation and Engagement, and Head of the Department of Mathematics, Statistics and Physics. She was a thought leader on a number of innovative projects and initiatives including supporting undergraduate research excellence. She has been guest editor of a number of mathematical sciences journals published by Springer Verlag, John Wiley & Sons and the American Institute of Physics and has been invited as keynote speaker on a number of occasions dealing with Mathematics, promoting Science, Technology and Innovation and topical issues in Higher Education. She has published widely in Mathematics on differential equations and their applications and continues to collaborate with South African and International Authors.