Title | Mathematical modeling of geophysical processes in a layer of an electrically conducting liquid of variable depth |
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Authors | V. K. Kazankov^{1}, S. E. Kholodova^{1}^{1}ITMO University |

Annotation | The boundary value problem of magnetic hydrodynamics is considered, which in the approximation of long waves of small amplitude is reduced to the integration of a single scalar equation for a modified function describing the perturbation of the free surface of a liquid layer. The solution of the obtained dispersion equation is reduced to the search for the roots of a polynomial of the sixth degree with complex coefficients. The article discusses a numerical method and an algorithm created on the basis of machine learning and an iterative numerical method that allows you to find different roots of a given polynomial. The analysis of the dependence of the solution on the Coriolis parameter, the wave number and the magnetic Reynolds number, which allow us to qualitatively and numerically assess the dynamics of the process, is carried out. |

Keywords | magnetic hydrodynamics of a rotating fluid, partial differential equations, mathematical modeling, magnetic Reynolds number |

Citation | Kazankov V. K., Kholodova S. E. ''Mathematical modeling of geophysical processes in a layer of an electrically conducting liquid of variable depth'' [Electronic resource]. Proceedings of the XV International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 15-18, 2021). Saransk: SVMO Publ, 2021. - pp. 149-155. Available at: https://conf.svmo.ru/files/2021/papers/article03.pdf. - Date of access: 22.06.2024. |

**© SVMO, National Research Mordovia State University, 2024**

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