Degenerate four-photon parametric processes and vector solitons

In the present work we investigate more precisely the influence of degenerate four-photon parametric process on the soliton propagation and the periodic exchange of energy between elliptically polarized waves. The obtained nonlinear dispersion relations describe clear physical picture of balance between dispersion and different kinds of nonlinear phase modulations of linearly and circularly polarized solitons. In quasi-CW regime, the system of equations is analytically solved. The obtained solutions, in the form of Jacobi elliptic functions, describe evolution of the intensities of the components of the vector field.