Nilpotent Morse algebra and time evolution of certain associated coherent states

We provide the time evolutions of the linear and nonlinear coherent states for several systems characterized by different energy spectra, and we identify the regions in the parameter space where these systems behave closer to the classical systems. The Morse system is algebraically found within the frame of generalized Heisenberg algebra(GHA). We demonstrate that this system is described by a nilpotency condition. Then, we propose a construction of coherent states for the Morse oscillator.