Numerical analysis of the kinetic equation describing isotropic 4-wave interactions in non-linear physical systems

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Numerical analysis of the kinetic equation describing isotropic 4-wave interactions in non-linear physical systems. / Semisalov, B. V.; Medvedev, S. B.; Nazarenko, S. V. et al.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 133, 107957, 06.2024.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{36e99cb65acd492997f1627eba504d6b,

title = "Numerical analysis of the kinetic equation describing isotropic 4-wave interactions in non-linear physical systems",

abstract = "We develop a numerical method for solving kinetic equations (KEs) that describe out-of-equilibrium 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 right-hand 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.",

keywords = "Bose gas, Cauchy problem, Collocation method, Cubature formula, Inverse cascade of particles, Kinetic equation, Random fiber lasers, Rational approximations, Relaxation method, Wave turbulence",

author = "Semisalov, {B. V.} and Medvedev, {S. B.} and Nazarenko, {S. V.} and Fedoruk, {M. P.}",

note = "This work was done under the financial support of the Russian Science Foundation (project No. 22-11-00287). Sergey Nazarenko research on Wave Turbulence is founded by the Simons foundation grant (Award ID 651471).",

year = "2024",

month = jun,

doi = "10.1016/j.cnsns.2024.107957",

language = "English",

volume = "133",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Numerical analysis of the kinetic equation describing isotropic 4-wave interactions in non-linear physical systems

AU - Semisalov, B. V.

AU - Medvedev, S. B.

AU - Nazarenko, S. V.

AU - Fedoruk, M. P.

N1 - This work was done under the financial support of the Russian Science Foundation (project No. 22-11-00287). Sergey Nazarenko research on Wave Turbulence is founded by the Simons foundation grant (Award ID 651471).

PY - 2024/6

Y1 - 2024/6

N2 - We develop a numerical method for solving kinetic equations (KEs) that describe out-of-equilibrium 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 right-hand 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.

AB - We develop a numerical method for solving kinetic equations (KEs) that describe out-of-equilibrium 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 right-hand 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.

KW - Bose gas

KW - Cauchy problem

KW - Collocation method

KW - Cubature formula

KW - Inverse cascade of particles

KW - Kinetic equation

KW - Random fiber lasers

KW - Rational approximations

KW - Relaxation method

KW - Wave turbulence

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85187792910&origin=inward&txGid=2d10de3a493e0f53a319a23633e1d0e2

UR - https://www.mendeley.com/catalogue/0b2bd6a5-0498-3a2f-9046-4de0615d11f5/

U2 - 10.1016/j.cnsns.2024.107957

DO - 10.1016/j.cnsns.2024.107957

M3 - Article

VL - 133

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 107957

ER -

ID: 60875778