Two integrable differential-difference equations derived from NLS-type equation

Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr"oinger equation respectively. Multi-soliton solutions of the resulted semi-discrete systems are given through Hirota’s bilinear method. Elastic and inelastic interaction behavior between two solitons are studied through the asymptotic analysis. Dynamics of two-soliton solutions are shown with graphs.