Magnetoacoustic nonlinear periodic (cnoidal) waves and solitons are studied in magnetized electron-ion plasmas with inertial cold ions and warm electrons. Using the two fluid model, the dispersion relation of the magnetoacoustic waves is obtained in the linear limit and the wave dispersive effects appear through the electron inertial length. The well known reductive perturbation method is employed to derive the Korteweg-de Vries equation for magnetoacoustic waves in plasmas. The Sagdeev potential approach is used, and the cnoidal wave solution of magnetoacoustic waves is obtained under periodic boundary conditions. The analytical solution for magnetoacoustic solitons is also presented. The phase plane portraits are also plotted for magnetoacoustic solitons shown as a separatrix, and the cnoidal wave structure always lies within the separatrix. It is found that plasma beta, which depends on the plasma density, electron temperature, and magnetic field intensity, has a significant effect on the amplitude and phase of the cnoidal waves, while it also affects the width and amplitude of the magnetoacoustic soliton in plasmas. The numerical results are plotted within the plasma parameters for laboratory and space plasmas for illustration. It is found that only compressive magnetoacoustic nonlinear periodic wave and soliton structures are formed in magnetized plasmas.
Nonlinear magnetoacoustic waves in collisionless homogenous, magnetized quantum plasma is studied. Two fluid quantum magneto-hydrodynamic model (QMHD) is employed and reductive perturbation method is used to derive Korteweg de Vries (KdV) equation for magnetoacoustic waves. The effects of plasma density and magnetic field intensity are investigated on magnetoacoustic solitary structures in quantum plasma. The numerical results are also presented, which are applicable to explain some aspects of the propagation of nonlinear magnetoacosutic wave in dense astrophysical plasma situations.
Ion-acoustic shock wave propagation in dense magnetized plasmas with relative density effects of spin-up and spin-down degenerate electrons is studied. The ions are classical, and their dissipative effects on plasma dynamics are included via kinematic viscosity. The electrons with spin-up and spin-down states are taken as separate species. The quantum tunneling effects of electrons are also considered in equations of motions of electrons. The Korteweg de Vries Burgers (KdVB) equation is derived, which admits the shock solution. The KdVB equation is solved numerically to study the transition from shock with oscillatory trails at its wave fronts to the monotonic shock structure with respect to variations in different plasma parameters. The parametric role of the spin density polarization ratio in the propagation characteristics of the shock wave structure is discussed.
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