Numerical solutions of a variable-coefficient nonlinear Schrodinger equation for an inhomogeneous optical fiber

This paper investigates a variable-coefficient nonlinear Schriidinger equation for an inhomogeneous optical fiber. Numerical one- and two-solitonic envelopes of the electrical field via the fourth-order split-step Runge-Kutta, split-step Fourier and Runge-Kutta methods with equal grids in the tau axis and equal grids in the xi axis are graphically presented, respectively, where tau and xi represent the retarded time and normalized distance along the fiber. 2-norm of the relative errors between the analytical solutions under the Painleve integrability condition and numerical solutions are given, where the CPU time is also shown. Relative errors and CPU time of the numerical one- and two-soliton solutions with equal grids in the xi axis are bigger than those with equal grids in the tau axis, which does not mean that the results with equal grids in the xi axis are infeasible. Compared with the numerical solutions with equal grids in the tau axis, those with equal grids in the xi axis are closer to the analytical solutions without the Painleve integrability condition. With respect to the relative errors and CPU time, one could choose the split-step Fourier method to derive the numerical one-soliton solutions, while the numerical two-soliton solutions are gotten with the RK method. The attenuation coefficient makes the amplitudes of the solitons decrease, the group velocity dispersion coefficient leads to the periodic solitons, while the effect of the attenuation coefficient is more obvious than that of the nonlinearity parameter. Effects of eta(R,1) and eta(I,1) on the solitonic weak interaction between the two solitons are investigated: Solitonic weak interaction between the two solitons enhances with eta(R,1) and eta(I,1) increasing, where eta(R,1) and eta(I,1) are the frequencies of the two solitons. (C) 2018 Elsevier Ltd. All rights reserved.