Abstract
This paper revisits the study of optical solitons that is governed by one of the three forms of derivative nonlinear Schrodinger's equation that is also known as Chen-Lee-Liu model. This model is investigated by the aid of fully shifted Jacobi's collocation method with two independent approaches. The first is discretization of the spatial variable, while the other is discretization of the temporal variable. It is concluded that the method of the current paper is far more efficient and reliable for the considered model. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.