On astigmatic solutions of the wave and the Klein-Gordon-Fock equations   with exponential fall--off
  Highly localized explicit solutions to multidimensional wave and Klein--Gordon--Fock equations are presented. Their Fourier transform is also found explicitly. Solutions depend on a set of parameters, and demonstrate astigmatic properties. Asymptotic analysis for large and moderate time shows that constructed solutions have Gaussian localisation near a point moving with the group speed. 
Ignat V. Fialkovsky, Maria V. Perel, Alexander B. Plachenov
math-ph math.MP