Interaction of solitons with extended nonlinear defects.

The interaction of nonlinear Schrödinger solitons with extended inhomogeneities with modified nonlinear coefficients is investigated numerically. Decreased nonlinear coefficients act as nonlinear potential steps and yield transmission or reflection of the incoming soliton. For increased nonlinear coefficients (nonlinear potential wells) and a given range of initial velocities and nonlinearity mismatch, the scattering pattern exhibits periodically repeating regions of trapping and transmission as a function of the length of the inhomogeneity. It is shown that the escape of the soliton is due to a resonance between the period of the shape oscillations of the soliton inside the inhomogeneity and the length of the latter. The combined effect of overlapping linear and nonlinear potentials is also investigated.