Similarity solutions for high frequency excitation of liquid metal in an   antisymmetric magnetic field
  The aim of this paper is to investigate, as precisely as possible, a boundary value problem involving a third order ordinary differential equation. Its solutions are the similarity solutions of a problem arising in the study of the phenomenon of high frequency excitation of liquid metal systems in an antisymmetric magnetic field within the framework of boundary layer approximation. 
B. Brighi and J.-D. Hoernel