The 1st place for the best scientific publication in mathematics in 2024 is awarded to

Fetisov Dmitriy Anatolyevich, Professor, FN-12 Department

for the paper "On feedback linearization of multi-input nonlinear control systems via time scaling and prolongation", published in "European Journal of Control" (Q1, Scopus).

The paper shows that the problem of feedback linearization for a nonlinear vector control system using time scaling may be solved by constructing the Pfaffian system J naturally associated with the control system and eliminating the time differential from J. The author proves that the Pfaffian system I thus obtained is diffeomorphic to an extended Goursat normal form if and only if the control system may be linearized via feedback driven by time scaling. The author also proves that if there may be no feedback linearization via time scaling in the control system but there are coordinates in which the Pfaffian system I becomes an extended Goursat form, then the control system may be feedback-linearized via time scaling and prolongation. The paper demonstrates that in this case, either a one-fold or a total prolongation may arise.

2nd place

Savin Alexandr Sergeevich, Professor, FN-1 Department

for the paper "Motion of liquid particles in the field of 1:1 resonance nonlinear wave", published in "International Journal of Non–Linear Mechanics" (Q1, Scopus).

The paper examines wave motion in a fluid layer of finite depth described by Euler's equations for an ideal incompressible fluid. The ice sheet is simulated by a geometrically nonlinear elastic Kirchhoff-Love plate floating freely on the surface of the liquid. Trajectories of liquid particles under the ice sheet are found in the field of nonlinear surface travelling waves of small yet finite amplitudes, said waves being produced by a nonlinear periodic carrier wave focusing and defocusing. The carrier wave comprises a solitary wave packet (a monochromatic wave under the envelope, with a speed equal to that of the envelope) and a so-called "dark soliton" (a wave generated via nonlinear interaction of a kink and a periodic wave). The analysis uses explicit asymptotic expressions for solutions describing wave structures at the water-ice interface, such as the solitary wave packet and the dark soliton, as well as asymptotic solutions describing the velocity fields generated by these waves in the fluid column.

3rd place

Chetverikov Vladimir Nikolaevich, Professor, FN-12 Department

Pirogova Arina Dmitrievna, postgraduate student, FN-12 Department

for the paper "Quantitative indicators of controllability of nonlinear systems" in "Differential Equations" (Q2, Scopus).