Solving Nonlinear Schrödinger Equation Using Split-Step Fourier Method

This program utilizes the split-step Fourier algorithm to solve the nonlinear Schrödinger equation. The algorithm is based on Fourier transform principles, decomposing the nonlinear Schrödinger equation into a series of linear equations to obtain the final solution. The implementation involves discrete time and space discretization with appropriate boundary conditions applied at each computational step. The core algorithm operates by alternating between linear and nonlinear operators: the linear part is handled in Fourier domain using FFT operations, while the nonlinear part is computed in the spatial domain. This separation allows for efficient computation through specialized numerical techniques. Key implementation aspects include: - Time-step discretization using symmetric operator splitting - Spatial discretization with periodic boundary conditions - Fast Fourier Transform (FFT) for efficient domain conversion - Nonlinear term handling using exponential operator integration - Numerical stability considerations through step size optimization Additionally, we incorporate common numerical techniques and optimization strategies to enhance algorithm efficiency and accuracy, such as adaptive step sizing and spectral filtering. The program provides a straightforward yet effective approach for solving nonlinear Schrödinger equations, serving as a foundation for further research and applications in wave propagation and nonlinear optical phenomena.