Abstract: We develop a numerical method for solving kinetic equations (KEs) that describe out-ofequilibrium isotropic nonlinear four-wave interactions in optics, deep-water wave theory, physics of superfluids and Bose gases, and in other applications. High complexity of studying numerically the wave kinetics in these applications is related with the multi-scale nature of turbulence and with power-law behaviour of turbulent spectra in the Fourier space. When solving the Cauchy problem for KE, this leads to emergence of spectra with extremely steep gradients and to occurrence of singular points in the collision integral standing in the righthand side. To solve these problems, we develop special fast-convergent cubature formulas, highly-accurate rational approximations of the KE solution, and a new stable method for time marching. We apply the developed methods for solving the test problems of integration arisen from applications, for studying the wave kinetics in random fiber lasers and for analysing the Bose–Einstein condensation. In these applications we used KEs obtained from the Ginzburg–Landau and from the Gross–Pitaevskii equations.

Cite: Semisalov B.V. , Medvedev S.B. , Nazarenko S.V. , Fedoruk M.P.
Numerical analysis of the kinetic equation describing isotropic 4-wave interactions in non-linear physical systems
Communications in Nonlinear Science and Numerical Simulation. 2024. V.133. 107957 :1-19. DOI: 10.1016/j.cnsns.2024.107957 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Oct 31, 2023
Accepted:	Mar 5, 2024
Published online:	Mar 6, 2024
Published print:	Mar 15, 2024

Identifiers:

Web of science:	WOS:001207736600001
Scopus:	2-s2.0-85187792910
Elibrary:	66870034
OpenAlex:	W4392519907

Citing:

DB	Citing
OpenAlex	2
Scopus	3
Web of science	3

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