Transformation of sinusoidal electromagnetic and polarization waves into cnoidal waves in an optical fibre

It is shown that a sinusoidal signal wave can transform into a cnoidal (periodic) wave in an optical fibre if the power signal propagates in the fibre core. In this case the signal wave period increases, but the wave profile does not almost change. The signal wave gets the form of kink for the high-power signal. The wave transformation is determined by nonlinear effects in the fibre core. The linear modes of the fibre transform into the nonlinear ones under influence of cubic or higher nonlinear interactions of electromagnetic and polarization waves. These changes are described by the equation with sinusoidal nonlinearity for the polarization wave. The approximate and exact analytical solutions of the nonlinear equation are obtained.