Four-wave parametric oscillation in a transversely pumped system

The variational principle is used to derive a system of equations describing the four-wave parametric oscillation in a medium with a reactive cubic nonlinearity. In the case of a transversely pumped configuration the integrals of the system can be used to obtain an analytic solution of the problem. The steady-state above-threshold amplitude of the signal waves is limited by their phase self-modulation and it is close to the amplitude of the reference waves.