Abstract
An efficient algorithm, which exhibits a fourth-order global accuracy, for the numerical solution of the
normal and generalized nonlinear Schrödinger equations is presented. It has applications for studies of
nonlinear pulse propagation and spectral broadening in optical fibers. Simulation of supercontinuum generation
processes, in particular, places high demands on numerical accuracy, which makes efficient high-order schemes
attractive. The algorithm that is presented here is an adaptation for use in the nonlinear optics field of the
fourth-order Runge–Kutta in the Interaction Picture (RK4IP) method, which was originally developed for studies
on Bose–Einstein condensates. The performance of the RK4IP method is validated and compared to a number of
conventional methods by modeling both the propagation of a second-order soliton and the generation of supercontinuum
radiation. It exhibits the expected global fourth-order accuracy for both problems studied and is the most accurate
and efficient of the methods tested.
© 2007 IEEE
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