Advanced Mathematical Models and Integration Methods

This volume presents selected contributions from the seminar “Mathematical Models and Integration Methods,” highlighting recent advances in differential equations, mathematical modeling, and modern analytical techniques. The topics cover a wide range of problems, including vortex structures in ferromagnets, wave propagation in inhomogeneous media, reciprocal transformations of heat equations, nonlinear resonance phenomena, and composite beam analysis. The collection also includes studies on the exponential map of vector fields, sedeonic models in superconductivity, and transformations in relativistic systems. Most contributions are from leading Russian researchers, complemented by papers from international participants. The book is intended for specialists in applied mathematics, mathematical physics, and engineering disciplines interested in contemporary modeling approaches and integration methods.

The book contains:

• Most recent integration methods;
• Mathematical approaches applicable to nonlinear models;
• Contributions from prominent mathematicians.

Dr. Oleg Viktorovich Kaptsov, born on November 1, 1956, in Novokuznetsk, Russia, is a prominent figure in Mathematics and Hydrodynamics. Holding a Doctor of Sciences degree and the esteemed position of Professor, Dr. Kaptsov has dedicated his career to advancing our understanding of complex mathematical and hydrodynamic phenomena. Dr. Kaptsov began his academic journey at Novosibirsk University, where he pursued undergraduate studies in Mathematics and Mechanics from 1974 to 1979. He continued his education with postgraduate studies at the Lavrentjev Institute of Hydrodynamics in Novosibirsk from 1981 to 1984. Dr. Kaptsov's research career started as a junior researcher at the Institute of Theoretical and Applied Mechanics in Novosibirsk from 1985 to 1988, followed by a senior researcher position at the Computing Center of the Academy of Science in Krasnoyarsk from 1987 to 1994. Since 1994, he has been a leading researcher at the Institute of Computing Modelling, Academy of Science, Krasnoyarsk, and a Professor at Siberian Federal University (SFU, Krasnoyarsk). Dr. Kaptsov's research focuses on Differential Equations, Exact solutions of nonlinear partial differential equations, Continuous groups of transformations, and Inviscid Fluid dynamics, significantly contributing to advancing theoretical foundations in these areas. His recent publications since 2019 have gained significant attention, including investigations into Traveling Waves in Nondispersive Strongly Inhomogeneous Media, Dynamics of passive scalar in swirling turbulent far wakes, and General solutions of some linear equations with variable coefficients. Noteworthy works by Dr. Kaptsov include “Applications of Group-Theoretical Methods in Hydrodynamics” (a joint work with V. K. Andreev, V. V. Puckhnachov, and A. A. Rodionov) and “Integration Methods of Partial Differential Equations.” Dr. Kaptsov's dedication to advancing knowledge in Mathematics and Hydrodynamics has earned him respect and admiration, making him a formidable force in scientific inquiry.

Dr. Evgeniy Igorevich Kaptsov is a researcher with expertise in computational mathematics and fluid dynamics. He graduated from Kuban State Technological University in 2008 with a Master's degree in Computer Science. Dr. Kaptsov has over a decade of industry experience as a software developer in prominent retail and game development companies in Russia. He completed his PhD in Computational Mathematics in 2020 at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, where he developed new methods for constructing invariant finite-difference schemes for one-dimensional gas dynamics and shallow water equations as a Research Assistant. Since 2018, he has been a researcher at the School of Mathematics, Suranaree University of Technology, Thailand, under the guidance of Professors V.A. Dorodnitsyn and S.V. Meleshko. Dr. Kaptsov has made significant contributions to the field, focusing on conservation laws, invariant solutions, and numerical implementations for various mathematical models, as evidenced by his numerous publications in esteemed journals.