  This paper studies the dynamical behavior near a new family of explicit
self-similar solutions for the one dimensional Born-Infeld equation. This
quasilinear scalar field equation arises from nonlinear electromagnetism, as
well as branes in string theory and minimal surfaces in Minkowski spacetimes.
We show that both this model and the linear wave equation admit the same family
of explicit timelike self-similar blow up solutions, meanwhile, Lyapunov
nonlinear stability of those self-similar blow up solutions are given inside a
strictly proper subset of the backward light cone.
