Elliptical solitons in the dissipative Lugiato-Lefever equation

The formation and stability of dissipative solitons in the vector Lugiato-Lefever model are considered for the case when only one of the field components (polarization) is excited by the external coherent pump. It shown that linearly polarized solitons can be destabilized because of the growth of the excitations belonging the orthogonal polarization. Vector (elliptically polarized) solitons bifurcating from linearly polarized ones are found, and the stability and dynamics of the vector solitons are studied.