Solving nonlinear Schrodinger equation using stable implicit finite difference method in single‐mode optical fibers

The different nonlinear Schrodinger equation (NLSE) types describe a lot of interesting physical phenomena. The NLSE which models the light in single‐mode nonlinear optical fibers propagation when the wave packet drift and attenuation are neglected has been studied. A stable implicit scheme is developed to solve this equation. The accuracy of this method is second order over both the space and time. By using von‐Neumann stability analysis, we have proven that our scheme is unconditionally stable. Numerically, many tests have been proceeded to present the scheme robustness. It is proven that the mass, momentum, and energy are conserved. The interaction between solitons with different directions has been studied. The effects of the factors of chromatic dispersion and self‐phase modulation on the solitons movement and conserved quantities as well as the relation between the factors have been discussed. It has been found that the physical parameters of self‐phase modulation and chromatic dispersion impacts are beneficial especially for fiber optical investigations.