Release:
2025. Vol. 11. № 3 (43)About the authors:
Gennadiy N. Efimov, Cand. Sci. (Tech.), Associate Professor, Department of Information Systems of Digital Economy, Russian University of Transport (MIIT), Moscow, Russia; efimov-mat@mail.ru, https://orcid.org/0000-0002-8636-4416Abstract:
Being a high-energy state of matter, plasma plays a key role in modern technologies, astrophysics, and controlled thermonuclear fusion. A central challenge lies in the analysis of nonlinear oscillations and waves in plasma, which can lead to the formation of singularities, such as gradient catastrophes or wave breaks. These phenomena are not only of theoretical interest for understanding nonlinear processes in plasma but also have practical implications. The object of the study is the Euler–Poisson system of equations, which serves as one of the fundamental models for describing plasma dynamics. This system can be modified to account for various physical factors, including magnetic fields, relativistic effects, and particle collisions. The aim of this work is to investigate the Euler–Poisson system describing nonlinear oscillations in plasma. The primary focus is on the conditions for the loss of smoothness in solutions within finite time.Keywords:
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