Exact solution of 1D magnetic Euler-Poisson equations arising in plasma physics

We report an exact space-time–dependent solution of 1D magnetic Euler-Poisson (mEP) equations. The mEP equations analyzed here describe the dynamics of upper-hybrid oscillations (UHOs) in a magnetized plasma. The obtained solution exhibits nonlinear behaviour of electron oscillations in a magnetic field within a spatially confined plasma. Our findings may provide a theoretical framework for future studies of nonlinear phenomena in plasmas and related charged particle systems.