A New Derivation of Exact Solutions for Incompressible Magnetohydrodynamic Plasma Turbulence

The objective of this paper is to study the propagation of nonlinear, quasi-parallel, magnetohydrodynamic waves of small-amplitude in a cold Hall plasma of constant density. Magnetohydrodynamic equations, along with the cold plasma were expanded using the reductive perturbation method, which leads to a nonlinear partial differential equation that complies with a modified form of the derivative nonlinear evolution Schrodinger equation. Exact solutions of the turbulent magnetohydrodynamic model in plasma were formulated for the physical quantities that describe the problem completely by using the complex ansatz method. In addition, the complete set of equations was used taking into account the magnetic field, which can be considered to be constant in the x-direction to create stable vortex waves. Vortex solutions of the modified nonlinear Schrodinger equation (MNLS) were compared with the solutions of incompressible magnetohydrodynamic equations. The obtained equations differ from the standard NLS equation by one additional term that describes the interaction of the nonlinear waves with the constant density. The behavior of both the velocity profile and the waveform of pressure were studied. The results showed that there are clear disturbances in the identity of the velocity and thus pressure. The identity of both velocity and pressure results from that a magnetic field is formed.

Automated summary

This paper investigates the propagation of nonlinear, quasi-parallel magnetohydrodynamic waves in a cold Hall plasma of constant density. By using the reductive perturbation method, a nonlinear partial differential equation compliant with a modified form of the derivative nonlinear evolution Schrodinger equation was derived. The study also considers the stable vortex waves created by a magnetic field constant in the x-direction, and shows disturbances in the identity of velocity and pressure due to the presence of the magnetic field.