  In this work we apply the Adomian decomposition method combined with the
Laplace transform (LADM) in order to solve the 1-dimensional nonlinear
Schrodinger equation whose nonlinear term presents a nonlinear defocusing
strength that varies in the spatial direction. The suggested iterative scheme
(LADM) finds the solution without any discretization, linearization or
restrictive assumptions. Finally, three numerical examples are presented to
demonstrate the reliability and accuracy of the method.
