Saddle-node bifurcation and modulational instability associated with the pulse propagation of dust ion-acoustic waves in a viscous dusty plasma: A complex nonlinear Schrödinger equation

Abstract

Using the standard reductive perturbation technique, a nonlinear Schrödinger equation (NLSE) with complex coefficients is derived in a dusty plasma consisting of positive ions, nonthermal electrons, and charged dust grains. The effect of ion kinematic viscosity is taken into consideration, which makes the coefficients of NLSE complex. By means of a matching approach, the appearance mechanism of static pulses through a saddle-node bifurcation in the complex nonlinear Schrödinger equation is studied analytically. The analytical results are in good agreement with the direct numerical simulation. The modulational instability analysis is carried out for the dust ion-acoustic envelope solitary waves. The important role of the real part of the complex group velocity in the propagation of the one-dimensional wave packets in homogeneous active medium is predicted.