鈥� a seminar of the Mathematical Center in Akademgorodok and the Sobolev Institute of Mathematics of the Siberian Branch of RAS (IM SB RAS), the purpose of which is to give students a general idea of the areas of research carried out by scientists from the Novosibirsk Scientific Center, as well as Russia and the world. The peculiarity of the seminar is that the emphasis in the talks is on the accessibility of the presentation of the material to a wide circle of the mathematical community, and only then on the detailing of the mathematical content.
At the next Colloquium on March 9 at 4:30 pm Boris V. Semisalov (Candidate of physical and mathematical sciences, Senior researcher of the Laboratory of Computational Problems of Mathematical Physics Problems IM SB RAS, Associate professor of the Chair of Differential Equations of the Department of Mathematics and Mechanics of NSU) will give a talk "On turbulent cascades in physical systems described by the nonlinear Schr枚dinger equation". The seminar will be held in room 417 of the IM SB RAS.
More details can be found on the website of the Mathematical Colloquium .Revealing the mechanisms of origin and development of turbulent flows is one of the main open problems of modern physics. The application of mathematical methods here makes it possible to detect and describe the processes of energy transfer and other invariants between disturbances of different scales. Such processes are called cascades. They arise in non-linear systems and serve as the key to understanding the early evolution of the Universe, the reasons for the anomalous heating of the solar corona, the emergence of "killer waves" in the oceans, and a significant number of other phenomena.
During the report, we will discuss the latest results of analytical and numerical studies of cascade processes in physical systems described by the three-dimensional Schr枚dinger equation with cubic nonlinearity. This equation is used in optics, cosmology, superfluidity models and Bose-Einstein condensation. The interaction of waves in such applications can be described by a kinetic integro-differential equation. We have studied the evolution of the solution of this equation, calculated self-similar regimes, and obtained exact stationary solutions corresponding to cascade processes.
The results were obtained in collaboration with Y. Zhu, G. Krstulovic, S. V. Nazarenko, V. N. Grebenev and S. B. Medvedev.
