Controllable trajectory and shape of Hermite-Gaussian soliton clusters

We introduce a kind of Hermite-Gaussian (HG) solitons, with off-axis and chirp parameters, propagating in nonlinear media with harmonic potential wells. The general formula for the trajectory of solitons is derived, and the propagation properties also be analyzed. The results shown that the off-axis HG solitons can present three different propagation states (including serpentine, elliptically and circularly spiral trajectory) depending on the value of the chirp parameter. Accordingly, we propose the concept of cluster composing of several HG solitons. The cluster shape depending on the off-axis parameters of each constituent soliton, and the chirp parameters also play important roles in the evolution of the clusters. Some typical examples are numerically demonstrated for graphically illustrating the propagation properties. Obviously, the controllable trajectory and shape of clusters may be applied in optical communication and particle controlling.