Modulational instability criterion for optical wave propagation in birefringent fiber of Kundu–Eckhaus equation

Abstract We study the modulational instability of nonlinear wave propagation in birefringent fiber of the Kundu–Eckhaus equation without four wave mixing term and analysis the effect of self phase modulation and cross phase modulation. The model of Kundu–Eckhaus equation in the absence of four wave mixing term are consider and apply the linear stability analysis to the Kundu–Eckhaus equation. Modulational instability criteria are found from linearized equations for small perturbations. Using modulational instability criteria, the self phase modulation and cross phase modulation effects on optical wave propagation in birefringent fiber are discussed.