Variable mesh difference schemes for solving a nonlinear Schrödinger equation with a linear damping term

This paper describes moving variable mesh finite difference schemes to numerically solve the nonlinear Schrödinger equation including the effects of damping and nonhomogeneity in the propagation media. These schemes have accurately predicted the location of the peak of soliton compared to the uniform mesh, for the case in which the exact solution is known. Numerical results are presented when damping and nonhomogeneous effects are included, and in the absence of these effects the results were verified with the available exact solution.