Dark ring soliton in two-dimensional nonlinear self-defocusing medium

We investigate the control of dark ring solitons with multi-layer ring-shapes, which are the one- and two-soliton solutions of the Korteweg-de Vries (KdV) equation. By using the reductive perturbation method, a cylindrical KdV equation for the two-dimensional self-defocusing nonlinear Schrödinger (NLS) equation is obtained, which possesses dark soliton solutions. By picking different orders of solutions of the KdV equation, the profiles of the intensity of the dark nonlinear waves display multi-layer ring-shapes, and can be controlled by the initial phase and the amplitude. Our results are expected to provide a theoretical basis for the control of dark ring solitons in nonlinear medium.