哈尔滨工业大学（深圳）学术讲座

演讲人Speaker：Semisalov Boris

题目Title: Numerical analysis of the wave kinetics in physical systems described by the nonlinear Schrodinger equation

时间Date：2026年6月11日      Time：10:00-11:00

地点Venue：H栋302室

内容摘要Abstract：

We develop a new approach for numerical analysis of the four-wave kinetic equation (KE) describing weakly-nonlinear isotropic interaction of waves in physical systems described by the nonlinear Schrodinger equation (NLS). Such systems arise in optics, cosmology, superfluidity and Bose–Einstein condensation. We verify the predictions of the wave turbulence theory for the latter application by solving numerically the NLS and the respective KE and by comparing their spectra. We get highly-accurate correspondence of the spectra in the time interval equal to doubled characteristic time of evolution of the spectrum. For the direct cascade of Bose gas energy and the inverse cascade of particles we derive and verify numerically the stationary solutions of Kolmogorov-Zakharov type including constant factors and logarithmic correction. This correction enables us to explain the inconsistence between theoretical predictions and experimental data from [Navon et al. Nature. 2016] and [Navon et al. Nature Phys. 2021].

These results were obtained thanks to new numerical method based on the high-order polynomial and rational approximations and original combination of the collocation and relaxation techniques, which enabled us to perform simulations in the frequency ranges of the width 107 and higher.

个人简介(About the speaker):

Semisalov Boris graduated from Novosibirsk State University in 2010, in 2011 got PhD in Applied Mathematics. From 2012 till 2020 worked as a researcher and senior researcher at Federal Research center for Information and Computational Technologies (Novosibirsk, Russia); from 2021 to 2025 - at Sobolev Institute of Mathematics SB RAS (Novosibirsk, Russia). In 2025 defended the Doctor of Science Theses in Mathematics and Physics at Keldysh Institute of Applied Mathematics RAS (Moscow, Russia). Now Semisalov Boris is associate professor at Shenzhen MSU-BIT University.

Semisalov Boris is author and co-author of more than 110 scientific papers and 4 patents for software packages. Under his leadership two project of Russian Science Foundation (Presidential program of research projects implemented by leading scientists, including young scientists) were successfully implemented in 2017–2019 and in 2020–2022. Under his supervision 11 students obtained their bachelor and master degrees.

Scientific interests of Semisalov Boris are focused on mathematical modelling and numerical analysis of complex non-linear phenomena including flows of viscoelastic polymer fluids and wave turbulence.