From the study of the dynamics for the ring-like soliton clusters,we find that there exists a critical value of the ring radius,d cr ,for the stationary rotation of the clusters with respect to the beam centre even in the presence of the relatively strong noise,and that the soliton clusters will not rotate but only undergo periodic collisions in the form of simple harmonic oscillator if the ring radius is large enough. We also show that the direction of the rotation can be opposite to the direction of phase gradient when the relative phase difference is within the domain 0 < |θ| < π,while along the direction of phase gradient when the relative phase difference is within the domain π < |θ| < 2π.
We study the propagation of (1+1)-dimensional spatial soliton in a nonlocal Kerr-type medium with weak nonlocality. First, we show that an equation for describing the soliton propagation in weak nonlocality is a nonlinear Schro¨dinger equation with perturbation terms. Then, an approximate analytical solution of the equation is found by the perturbation method. We also find some interesting properties of the intensity profiles of the soliton.
