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The stability of the solitary kinetic Alfven wave is investigated. In the one-dimensional fully nonlinear case the wave is shown to be stable against perturbations in the amplitudes.
The effect of the finite thickness of the shear layer on the Kelvin-Helmholtz instability of the Earth's magnetopause boundary is investigated. The thickness of the layer stabilizes the boundary with respect to short wavelength perturbations, which were previously found to be unstable in the zero thickness analysis. Compressibility effects further stabilize the layer. The effects of the magnetic field on the instability are also discussed.
The effect of electron collisions on reducing the wave-breaking amplitude of resonantly-driven electrostatic fields in a cold plasma is investigated. By means of a simple theory collisions are shown to compete with wave-breaking in dissipating wave energy.
The influence of temperature perturbations on the propagation and stability of low frequency waves in a weakly collisional plasma is analyzed. Temperature oscillations in general reduce the stability of ion acoustic waves. It also tends to lower the magnitude of the critical current necessary for triggering the instability. In the case of drift waves its effect is to change the destabilizing role of electron-ion collisions in the isothermal model into a damping influence.
The long time behavior of a monochromatic, finite amplitude shear Alfven wave is studied by means of the Krylov-Bogoliubov-Mitropolsky perturbation technique. The plasma model is assumed to be described by the linearly non-dispersive, ideal magnetohydrodynamic equations. Non-linear coupling between the Alfven pump wave and a free sound wave gives rise to forced magnetic sidebands. It is shown that the Alfven pump wave as well as the magnetic sidebands steepen up in the long time scale.
It is found that in a plasma with [beta] > 1 a finite amplitude ion acoustic wave is unstable and decays into two shear Alfven waves propagating in opposite directions. The threshold and growth rate of the instability are determined.
The Schrodinger equation with exponential nonlinearity is solved in the time-independent case. The solutions are compared with those obtained from the case with cubic nonlinearity.
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