RUDN University mathematician first described the movement in a flat strip of plasma
The Zakharov-Kuznetsov equation is a one-function equation of two variables x and y. For physics, x is the direction of wave propagation, and the deformation of the medium occurs along the perpendicular direction y. For example, an oscillation of the guitar string looks like the wave runs down the string, while the oscillations occur perpendicular direction relative to the run of the wave.
There are a large number of results that describe solutions of the Zakharov-Kuznetsov equations in the case when there are no constraints on y. But the question of wave propagation in the strip — when y is limited — was almost not studied until recently. And this is although such a statement of the problem has a physical meaning, and therefore potential applications.
RUDN University mathematicians dealt with the Zakharov-Kuznetsov equation in the strip. They examined three main cases — when there are no oscillations on the boundary of the strip, when there is no current on the same boundary and when the boundary conditions are periodic in structure. The latter case corresponds to the propagation of waves in a medium whose structure is periodic in x.
In all these cases mathematicians managed to prove theorems of existence and uniqueness of solutions. For systems of partial differential equations, which include the Zakharov-Kuznetsov equation, such equations are very rare.
These results are the first for solutions of the equation with initial conditions in the strip. Flat plasma flows with boundary conditions, which were considered by RUDN University scientists, can occur in physics and astrophysics.
The Zakharov-Kuznetsov equations belong to a wider category of equations known as the Korteweg-de Vries equations. In the study of this category of equations for the first time, it was possible to describe solitons — waves whose shape does not change during movement. Physicists consider solitons as a tool for modern optical data transmission systems. The study of solitons, which can arise in the Zakharov-Kuznetsov equations, is one of the options for the development of the work done by RUDN University mathematicians.
Scientists from the Winogradsky Institute of Microbiology RAS, RUDN University, St. Petersburg State University and the Tyumen Scientific Centre SB RAS studied the microbial communities from several lakes of the Yamal Peninsula. It turned out that methanotrophs (bacteria that use methane as a source of energy) consume methane more actively in the deep mature lakes of the peninsula than in small thermokarst lakes. In this regard, methane emissions into the atmosphere from the surface of deep lakes are low, and only small (relatively younger thermokarst lakes with constitutional ground ice) can make a significant contribution to methane emissions in the north of Western Siberia. Thus, bacteria perform an important function for the climate balance — they reduce the emission of methane into the atmosphere.
RUDN University physicists have described the conditions for the most efficient operation of long mirror-based variant of cyclotron in the autoresonance mode. These data will bring better understanding of plasma processes in magnetic traps.
Chemists from Russia and the USA have improved the method of creating bioactive indole-acetonitrile compounds. Previously, in the course of their synthesis, by-products were obtained — a new method allows them to be avoided. This increases the yield of the final product to 81%.