  We consider a scalar Fermi-Pasta-Ulam-Tsingou (FPUT) system on a square 2D
lattice with a cubic nonlinearity. For such systems the NLS equation can be
derived to describe the evolution of an oscillating moving wave packet of small
amplitude which is slowly modulated in time and space. We show that this NLS
approximation makes correct predictions about the dynamics of the original
scalar FPUT system for the strain and the displacement variables.
