  In this article we study global in time (not necessarily small) solutions of
the equation for the Higgs boson in the Minkowski and in the de Sitter
spacetimes. We reveal some qualitative behavior of the global solutions. In
particular, we formulate sufficient conditions for the existence of the zeros
of global solutions in the interior of their supports, and, consequently, for
the creation of the so-called bubbles, which have been studied in particle
physics and inflationary cosmology. We also give some sufficient conditions for
the global solution to be an oscillatory in time solution.
