  In this paper, we study the characteristic initial value problem for a class
of nonlinear wave equations with data on a conic light cone in the Minkowski
space $\mathbb{R}^{1+3}$. We show the existence of local solution for a class
of singular initial data in the sense that the standard energy could be
infinite and the solution may blow up at the conic point. As an application, we
improve our previous result on the inverse scattering problem for the
Maxwell-Klein-Gordon equations with scattering data on the future null
infinity.
