Omnipresent instability criterion of birefringent Kundu-Eckhaus model with nonic nonlinearity

Abstract

This paper intends to present an investigation of the ultra shortpulse propagation under the nonlinear birefringent Kundu-Eckhaus (KE) model. The dynamics of modulational instability(MI) is revealed with the linear stability analysis of the KE equation with higher-order, the cubic, and nonic nonlinearity effects. The role of cubic-nonic nonlinearity on MI gain spectra in KE fiber system with self and cross phase modulation is studied for the first time. The impact of nonic nonlinearity is shown to be much more prominent over its cubic-quintic counterpart. The presence of cubic-nonic combo nonlinearity lets the MI gain profile to be adjusted with the rate of self-phase modulation (SPM). This new MI gain growth dynamics controlled by the SPM parameter will be useful on soliton generation in birefringent KE fiber media.