The large nonlinearity scale limit of an information-theoretically   motivated nonlinear Schrodinger equation
  A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in the regime where the nonlinearity length scale is large compared to the deBroglie wavelength; just as in the perturbative regime, the equation again displays some universality. We also briefly discuss stationary solutions to a naturally induced discretisation of that equation. 
Le-Huy Nguyen, Hai-Siong Tan and Rajesh R. Parwani