Abstract:
The propagation of singularities for nonlinear wave equations, that is, the relation
between the singularities of the initial data and the singularities of the solution is
well understood. In this studyWe prove that smooth solutions develop singularities
in nite time. We construct exact traveling wave solutions with cusp singularities,
and use them to illustrate a phenomena of accumulation and annihilation of
oscillations in sequences of solutions with bounded energy. The result is that,
true locally, and if the solution is global, then it is also true globally
