Two Special Solutions of the Non-ideal Magnetohydrodynamics

A special transformation is found to solve the Magnetohydrodynamic equations, by which two classes of exact analytic time-dependent solutions of magnetic annihilation for incompressible magnetic fluid have been obtained. The solutions derived here possesses scaling property with time t as the scale factor. We find that the current can perform the soliton-like behaviour in the case of asymmetric inflow. The relevant evolution characteristics in the process of magnetic annihilation are also revealed.