Weak wave generation control in variational wave equation

Nonsmooth solutions to multiple integral variational problems are considered. Using the method of singular characteristics (MSC) an ODE system is derived describing the propagation of weak waves (jumps of the solution's gradient). Special consideration is given for so-called variational wave equation, where weak waves are generated by singularities in the initial data. The number and the character of the arising waves and the phenomenon of bifurcation of the weak waves (singular lines) are studied using analytical and numerical methods.