NLS approximation for a scalar FPUT system on a 2D square lattice with a cubic nonlinearity

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.