Robust dynamics of soliton pairs and clusters in the nonlinear Schrödinger equation with linear potentials

We demonstrate interesting dynamics of soliton pairs and clusters in the (2 + 1)-dimensional nonlinear Schrödinger equation with self-focusing Kerr nonlinearity and linear potentials. We display regular oscillation and rotation of such multidimensional solitary structures in our model, achieved by the proper choice of simple potentials. By utilizing linear stability analysis, we establish that these soliton pairs and clusters are completely robust, and the solitons do not experience any distortion during the perturbed propagation, even when the potentials evolve along the propagation direction. Note also that both the oscillating and rotating periods of soliton pairs and clusters can be easily controlled by the parameters of external potentials.