Abstract
We address the dynamics of fundamental and higher-order dark solitons on the intense parabolic background in a planar graded-index waveguide with self-defocusing nonlinearity. It is shown that dark solitons on the parabolic background can propagate stably, and feature the properties similar to dark solitons for standard nonlinear Schr\"odinger equation. We present an approximate solution for dark soliton on a parabolic background, and discuss its motion trajectory. In addition, the interaction between neighboring dark solitons on parabolic background is investigated.
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