Traveling Wave Solutions of the Incompressible Ideal Hall Magnetohydrodynamics**Supported by the National Natural Science Foundation of China under Grant No 11375190.

Abstract

The solutions of incompressible ideal Hall magnetohydrodynamics are obtained by using the traveling wave method. It is shown that the velocity and magnetic field parallel to the wave vector can be arbitrary constants. The velocity and magnetic field perpendicular to the wave vector are both helical waves. Moreover, the amplitude of the velocity perpendicular to the wave vector is related to the wave number and the circular frequency. In addition, further studies indicate that, no matter whether the uniform ambient magnetic field exists or not, the forms of the traveling wave solutions do not change.