Nonlinearity saturation as a singular perturbation of the nonlinear Schrödinger equation (Q2794980)

This paper concerns modulation and solitary wave interaction in the well-known cubic nonlinear Schrödinger equation. The paper uses multiple scale analysis and matched asymptotic techniques, as well as numerical experiments, to investigate the effect of a singular perturbation induced by small nonlinearity saturation. The authors find that the interactions of solitary and ambient waves are governed mainly by an eigenfunction which arises as a result of linearization about the solitary wave. The authors consider both the cases of one and two transverse dimensions. To overcome the difficulty for numerical simulation, the authors derived free boundary (in one dimension) and free singularity (in two dimensions) reductions and verified it numerically.