Travelling Wave Solutions of a Simple Non-Local Burgers-Like Equation
  A Lax pair consisting of the Forsyth-Hopf-Cole transformation and a linear differential (in time) - difference (in continuous space) equation generates the whole hierarchy of the Burgers equation and admits exact moving front solutions. This model mimics finite-distance spatial correlations or nearest neighbor interactions in a physical situation 
Alex Veksler and Yair Zarmi