Bifurcation Analysis of Dust Acoustic Waves in a Negatively Charged Dust Plasma With Regularized \((\kappa )\)-distributed Electrons-ions

A precise theoretical consideration of dust acoustic solitary (DAS) waves in a negative dust plasma with regularized \(\kappa \)-distributed (RKD) electrons and ions is presented. The linear and nonlinear analyses are studied. The KdV equation appropriate for depicting DAS waves is derived. The bifurcation concept of planar dynamical system (PDS) and Sagdeev potential analysis are used. The Jacobi elliptic function expansion approach for solving the KdVE is applied, which yields three analytical solutions to the solitary waves based on the system parameters. The DAWs are investigated by using four techniques to get a comprehensive awareness. It is found that such potential demonstrates a rarefactive solitary wave in the mesosphere zone. The effects of plasma parameters (such as electron temperature \(T_e\), cutoff \(\delta \), and electron density) on the DAWs are illustrated in 2D-3D, contour plots and phase portraits. Also, we introduced a novel comparison of the RKD and the standard \(\kappa \) distribution (SKD) in DAWs, where we extracted that the velocity of DAWs in the case of SKD is faster than in the case of RKD. The results from this work are expected to contribute to the in-depth understanding of the instability and propagation of the nonlinear DAWs in the Earth’s mesosphere zone and in the astrophysical plasma in general.