Think it through!

Graduated with honors from the Peoples’ Friendship University named after Patrice Lumumba in the specialty of «Mathematics». He was awarded the qualification of «Mathematician. Lecturer of mathematics in higher and secondary learning establishments». He was also awarded the qualification of «Translator from French into Russian».

Post-graduate student at the P. Lumumba Peoples’ Friendship University.

Candidate thesis “Method of Ostrogradskii and inverse problems of mechanics” was defended.

Staff member of the computing center of the Peoples’ Friendship University, senior lecturer.

Scientific trip to the University of California, Santa Barbara (USA).

Senior lecturer, associate professor in the Department of Mathematics and Informatics at the P. Lumumba Peoples’ Friendship University.

Doctoral thesis “Mathematical methods of mechanics of infinite-dimensional non-potential systems” for the degree of Doctor of Physics and Mathematics was defended at the M.V. Lomonosov Moscow State University.

Professor in the Department of Mathematical Analysis.

Academic title Professor was awarded.

Professor in the Department of Mathematical Analysis and Theory of Functions.

Professor of the S.M. Nikol’skii Mathematical Institute.

Gratitude of the Federal Agency for Education.

The breastplate and honorary title “Honorary worker of higher professional education of the Russian Federation”.

Honorary badge “Veteran of the RUDN”.

### Teaching

- V.M. Savchin worked out a number of new special courses for master's students, in particular:
- “Variational methods for the study of operators” (direction “Functional Methods in Differential Equations and Interdisciplinary Research”),
- “Inverse problems of the calculus of variations” (direction “Functional Methods in Differential Equations and Interdisciplinary Studies").

- Courses at the RUDN University:
- “Mathematical analysis” (direction “Applied Mathematics and Informatics”) for bachelor’s students,
- “Inverse problems of the calculus of variations” (direction “Functional Methods in Differential Equations and Interdisciplinary Research”) for bachelor’s students.

### Science

**Author of monographs:**

- Mathematical methods of mechanics of infinite-dimensional systems. M.: UDN, 1991, 237 p.,
- Variational principles for nonpotential operators //Results of science and technology. Contemporary Problems of Mathematics. Latest Achievement. M.: VINITI, 1992.Vol. 40. p. 3-178 (co-authors: Filippov V. M., Shorokhov S. G.) (translated and published in the USA).
- Research is closely linked with the works by G. Helmholtz, G. Birkhoff et al. on variational principles for finite-dimensional systems. The problem of the extension and development of their results to the case of infinite-dimensional systems was of theoretical and practical interest. It is interrelated with the problems of modern Hamiltonian mechanics, the existence of solutions to inverse problems of the calculus of variations for given equations and such algebraic structures as Lie algebras and Lie-admissible algebras. Major works are devoted to development of mathematical methods of mechanics of infinite-dimensional systems, development of methods for constructing variational formulations of the equations of motion of infinite-dimensional nonpotential systems and their application to such specific problems as the representation of evolution equations in the form of Hamilton's equations, the introduction of Poisson brackets and symmetric brackets in Eulerian and non-Eulerian classes of functionals, the search of algebraic structures associated with the equations of motion, finding symmetries and first integrals of evolution equations.

**V.M.Savchin:**

- Obtained a general criterion for the B-potentiality of operators with respect to local bilinear forms.
- Developed constructive methods of determination of integral variational principles for wide classes of equations of motion of infinite-dimensional nonpotential systems using Eulerian and non-Eulerian classes of functionals.
- Established the connection of equations of motion of nonpotential systems with different Poisson brackets and Lie-admissible algebras and on this basis extended the scope of application of classical Hamilton's mechanics.
- Obtained the operator equation - an analogue of ordinary Birkhoff’s differential equations - and established its significance in the mechanics of infinite-dimensional systems. Found the necessary and sufficient conditions for the representation of the given evolutionary equations in the form of Birkhhoff’s operator equation and obtained the formulas for the construction of the corresponding operators.
- Extended the methods of investigation of canonical equations of the rank greater than zero to infinite-dimensional nonpotential systems.
- For the first time ever formulated the inverse problem of the calculus of variations for a very general system of partial differential difference equations and obtained the conditions of its potentiality.
- Worked out an operator approach providing a unique methodology for the investigation of a number of properties of the equations of motion of both finite dimensional and infinite-dimensional systems.
- Theoretical results are applied, in particular, to the system of Navier-Stokes equations describing the flow of liquids, to the Korteweg-de-Vries equation describing nonlinear waves, in studies of a number of dissipative systems.

### Scientific interests

- variational principles for nonpotential operators,
- inverse problems of variational calculus,
- symmetries,
- the relationship of dynamical systems with algebraic structures.