  We study the Cauchy problem of higher dimensional Einstein-Maxwell-Higgs
system in the framework of Bondi coordinates. As a first step, the problem is
reduced to a single first-order integro-differential equation by defining a
generalized ansatz function. Then, we employ contraction mapping to show that
there exists the unique fixed point of the problem. For a given small initial
data, we prove the existence of a global classical solution. Finally, by
introducing local mass and local charge functions in higher dimensions, we also
show the completeness property of the spacetimes.
