Coupled-generalized nonlinear Schr?dinger 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 Schr?dinger 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.