Effect of polarization on the trajectory of dissipative solitons

We show that the optical magnus effect for dissipative solitons is determined not only by the helicity but also by the topological index, i.e., by the magnetic quantum number or by the projection of the soliton orbital moment on its trajectory. In the case of inhomogeneous media, we find a relation between the optical magnus effect and the nonholonomy of the field of unit vectors tangent to the trajectory.