Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

I will discuss the precise relationship between characteristic Cauchy data for partial differential equations (PDEs) and certain singularities of solutions called fold-type singularities. If we interpret a solution as a wave, then a fold-type singularity can be interpreted as a wave front. I’ll show that every PDE defines a new equation describing the propagation of such wave fronts. I will use the geometric language of jet spaces, so all the discussion will be manifestly coordinate independent. This is a review talk and I don’t claim any originality on the subject.

For the link please write to konieczn at fuw.edu.pl