Wellposedness results for the short pulse equation
  The short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the homogeneous initial boundary value problem and the Cauchy problem associated to this equation are studied. 
G.M. Coclite and L. di Ruvo
math.AP