Year: 2025
Type: article
Abstract: An exact solution of the collisionless time-dependent Vlasov equation is found. For the first time in a century, an analytical solution to the one-dimensional time-dependent Vlasov–Boltzmann equation has been found. It has been found that instead of the widely discussed damping, waves are subject to instability. By means of this solution, the behavior of the Langmuir waves in the nonlinear stage is considered. A symmetry method is found that allows us to establish the dependence on time of the desired quantity based on the dependence on the previous time. The analysis is restricted by the consideration of the first nonlinear approximation—keeping the second power of the electric strength. It is shown that in general the waves with finite amplitudes are not subjected to the damping. Conditions have been found under which waves can be unstable.
Source: Symmetry
DOI: 10.3390/sym17060809
Authors: Leon Kos, Ivona Vasileska, Davy D. Tskhakaya
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4410614744