Optical solitons based on N-coupled nonlinear Schrödinger equations and rational RBF partition of unity approach

Recently, several numerical methods based on the radial basis functions have been applied to solving differential equations. Many researchers have employed the radial basis functions collocation technique and its improvements to get more accurate and efficient numerical solutions. The Schrödinger equations have several applications in the optic and laser. Accordingly, several numerical procedures have been proposed. In this paper, we present a new numerical algorithm based on the time-split approach, and rational radial basis functions collocation method. First, a second-order time-split approach is used to discretize the time variable. In this stage, the linear and nonlinear terms are separated. The linear term is solved by using a collocation technique based on the rational approach, the radial basis functions, and the partition of unity. The nonlinear term is does not have a differential operator thus we will only insert approximate solutions into it. Finally, several numerical examples have been reported to show the stability, convergence, and accuracy of the proposed numerical algorithm.