Analytical Methods in Differential Equations

Conference Proceedings in Honor of Lev V. Ovsiannikov’s 105th Birthday Anniversary

Sergey V. Meleshko, Sibusiso Moyo, Eckart Schulz

• Publisher: De Gruyter
• Year: 2025
• Topic: Mathematics
• eBook ISBN:
  9783111570631
• Subtopic: Applied Mathematics
• Index: Mathematics

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.

Table of contents

• Title Page
• Copyright
• Contents
• A novel approximate analytical approach for the treatment of delay differential equations with fractional Caputo–Fabrizio derivative and application to an economic model
• Lie equivalence transformations and differential invariants for a generalized third-order Schrödinger partial differential equation with variable coefficients using real decomposition
• The existence of solitons in a freely interacting transonic viscous flow
• Integration by quadratures of Lie(–Hamilton) systems
• Integration of first-order ODEs by Jacobi fields
• On the modeling of curvilinear trajectories in inhomogeneous media
• On the Hamiltonian approach to delay ODEs
• Some properties of integrable Hamiltonian systems
• On the numerical and analytical solution of the Cauchy problem for ideal plasticity
• Using conservation laws for solving boundary value problems in deformable solid mechanics
• Symmetries of the extended Bogoyavlenskii generalized breaking soliton equation
• On the instability for one subclass of three-dimensional dynamic equilibrium states of the electron Vlasov–Poisson gas
• On the instability for one partial class of three-dimensional dynamic equilibrium states of the hydrogen Vlasov–Poisson plasma
• Exact solutions and automorphic systems of the geopotential forecast equation
• Application of the equivalence group for constructing invariant solutions of the inhomogeneous Boltzmann equations for a binary mixture of gases
• Stability of solutions of ordinary differential equations with control and perturbing actions under structural perturbations
• Regularizing factors for the Euler–Poisson equations
• The spectrum of a problem on the flow of a polymeric viscoelastic fluid in a cylindrical channel described by Vinogradov–Pokrovski model
• On exact solutions to the gas filtration problem in a thin poroelastic layer
• Lie symmetries, conservation laws, optimal system, and exact solutions of a (2+1)-dimensional time fractional parabolic equation