SOLITON-DEFECT COLLISIONS IN THE NONLINEAR SCHRODINGER-EQUATION

We report results of systematic numerical simulations of collisions be tween a soliton and an attractive defect described by the perturbing t erm in the nonlinear Schrodinger equation proportional to the S-functi on. This model has applications in nonlinear optics and other physical systems. In the parametric range where the defect's strength is of th e same order of magnitude as the soliton's amplitude, i.e., the intera ction is essentially nonlinear, only two outcomes of the collision are possible: transmission and capture. We have found a border between th e corresponding parametric regions. The border is represented in a uni versal form which does not depend on any free parameter. In this essen tially nonlinear regime of the interaction, the soliton keeps its inte grity, being transmitted or captured as a whole, practically without e mission of radiation. At larger values of the defect's strength, the i nteraction becomes nearly linear. In this case, the soliton is split i nto reflected, transmitted, and trapped wave packets. Using the corres ponding linear Schrodinger equation, we calculate analytically the sha res of the reflected and transmitted energy in the limiting case when the defect's strength and the soliton's velocity are essentially large r than its amplitude.