摘要
The study of similarity solutions is necessary for the understanding of the dynamical behaviour of the fluid in the high-frequency excitation of liquid metal embedded in an antisymmetric magnetic field. Such similarity solutions are governed by the third-order non-linear equation: f‴+m+1/2 ff″2 = 0 on (0, + ∞), subject to the boundary conditions f(0) = a ∈ ℝ, f′(0) = -1 and f′(+∞) = 0. The remaining unsolved case is for m ε (- 1, 0). In this paper, we will give an almost complete solution structure of this problem for m ε (- 1, 0), which complements earlier results in literature. © The Author 2011. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.