A New Construction for Scalar Wave Equations in Inhomogeneous Media
  The paper describes a formulation of discrete scalar wave propagation in an inhomogeneous medium by the use of elementary processes obeying a discrete Huygens' principle and satisfying fundamental symmetries such as time-reversal, reciprocity and isotropy. Its novelty is the systematic derivation of a unified equation which, properly tuned by a single parameter, leads to either the Klein-Gordon equation or the Schr\"{o}dinger equation. The generality of this method enables one to consider its extension to other types of discrete wave equations on any kind of discrete lattice. 
Samuel De Toro Arias and Christian Vanneste (LPMC Nice, CNRS)