Formation And Propagation Of Singularities In One Dimensional Nonlinear Wave Equation By Variational Method

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