Abstract

In a previous paper we described a unique numerical technique for resolving soliton propagation in nonlinear fibers. The numerical scheme is based upon an adaptive wavelet transform, adaptive in its ability to numerically resolve the effects of optical shock formation during self-steepening and singularity formation during optical beam self-focusing. The technique is referred to as the full adaptive wavelet transform (FAWT)¹. In this paper we shall further investigate the effects of higher-order nonlinearities in the modified nonlinear Schrödinger (NLS) equation, including their effects on singularity formation during self-focusing, using the FAWT. We will show that the technique may be used for any order of nonlinearity, with equally accurate results. While other methods which utilize the wavelet transform for solving nonlinear PDEs exist, these techniques are not full wavelet transforms, but instead rely upon a “split-step wavelet” method. Since the FAWT is a full wavelet transform, its accuracy is dependent only upon the number and type of wavelets used in the numerical scheme, and thus allows the user to control the accuracy of the solution, a much needed capability when resolving singularity formation during self-focusing

© 2002 Optical Society of America