Investigation of modulational instability in a coupled Kundu-Ekchaus equation in the presence of modified form of saturable nonlinearity

Abstract

We study the impact of modified saturable nonlinearity on modulational instability (MI) criteria in a coupled birefringent fiber using pulse propagation technique. Based on the standard linear stability method, we enquire nonlinear self/cross phase modulation on MI in a coupled Kundu–Eckhaus (KE) equation in the absence of nonlinear four-wave mixing expression. Using the modified KE equation, we study the role of modified form of saturable nonlinearity on MI in a birefringent KE model with the adjustable self/cross phase modulation coefficients. In the case of KE without nonlinear saturation and four-wave mixing, we observed that the cross phase modulation (XPM) has less induced the instability region on MI in coupled birefringent fiber system as compared to self phase modulation (SPM) case as shown in Ref. Parasuraman (2021). But, in saturable KE model showed different characteristics of MI and growth rate of profile in a coupled birefringent fiber system in the presence of particular emphasis values of the nonlinear terms as depicted in Ref. Mohanraj (2021). This study shows the novel results of MI criterion in a coupled KE birefringent media with the help of modified type of saturable nonlinearity and both SPM/XPM values. From the above-detailed discussion, the modified form of saturable nonlinearity plays an important role for MI generation in a KE birefringent media. However, the modified nonlinear saturation KE model more helps to generate ultrashort pulses and soliton or solitary wave in a coupled nonlinear birefringent fiber with the help of 3D images.