  This paper studies the self-similar singularity phenomenon of zero mean
curvature equation including Born-Infeld equation, space-like surfaces with
vanishing mean curvature equation and membrane equation which arises in string
theory and geometric minimal surfaces theory. We show that there exist new
explicit self-similar solutions for Born-Infeld equation, space-like surfaces
with vanishing mean curvature equation and membrane equation in Minkowski space
$R^{1+3}$ with respect to the radially symmetric case.
