Alternative split-step method for solving linearly coupled nonlinear Schrödinger equations

In this paper we introduce an alternative method for solving linearly coupled nonlinear Schrödinger equations by using a split-step approach. This methodology involves approximating the nonlinear part of the evolution operator, allowing it to be solved exactly, which significantly enhances computational efficiency. The dispersive component is addressed using a spectral method, ensuring accuracy in the treatment of linear terms. As a reference, we compare our results with those obtained using the Runge-Kutta method implemented using a pseudo-spectral technique. Our findings indicate that the proposed split-step method achieves precision comparable to that of the Runge-Kutta method while nearly doubling computational efficiency. Numerical simulations include the evolution of a single soliton in each field and a collision between two solitons, demonstrating the robustness and effectiveness of our approach.