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

This paper describes moving variable mesh finite difference schemes to nume rically solve the nonlinear Schrodinger equation including the effects of d amping and nonhomogeneity in the propagation media. These schemes have accu rately predicted the location of the peak of the soliton compared to the un iform mesh, for the case in which the exact solution is known. Numerical re sults are presented when damping and nonhomogeneous effects are included, a nd in the absence of these effects the results were verified with the avail able exact solution. (C) 2000 Elsevier Science Ltd. All rights reserved.