Coupled generalized nonlinear Schrodinger equations solved by adaptive step size methods in interaction picture

We extend two adaptive step size methods for solving two dimensional or multi dimensional generalized nonlinear Schrodinger equation (GNLSE): one is the conservation quantity error adaptive step control method (RK4IP CQE), and the other is the local error adaptive step control method (RK4IP LEM). The methods are developed in the vector form of fourth order Runge Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP LEM spends more time than RK4IP CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step size algorithms.