Different nonlinear dynamical behavior of dust-acoustic modes of a homogeneous plasma are examined. The plasma composed of negatively charged dust grains and nonextensive distribution electrons and ions. The evolution of the system is investigated using a 3-dimensional nonlinear Schrodinger (3D-NLS) equation. Different methods are used to explore the possible solutions of 3D-NLS equation using a bifurcation analysis and factorization method to obtain periodic, shocklike and explosive waves. Furthermore, rogue wave solution of the 3D-NLS equation is obtained to investigate the dependence of rogue wave profile on nonextensivity parameters. The present investigation can be relevance to the electrostatic structures in various dusty plasmas, such as Saturn’s E-ring.

The Earth's magnetosphere's modulational amplitude dust-ion-acoustic waves are studied. When the moon passes through the Earth's magnetotail, its dust grains may interact, causing these waves. The theoretical plasma model for this study includes positive ionospheric ion fluids, isothermal electrons, and fluid-negative dust grains on the moon. A perturbation technique derived the nonlinear Schrödinger equation, which exhibited dispersion and nonlinear effects. The nonlinear and dispersion term coefficients' polarity may predict stable and unstable pulse domains. A numerical study was performed to identify unstable pulse domains and their connections with bright and rogue unstable modes. The effects of critical plasma conditions on these pulses' basic features have been studied. This study showed that increasing the ratio of ions to electrons temperature and density reduces system nonlinearity. Consequently, shorter unstable pulses are formed. Amplification of plasma unstable waves results in an increase in their intensity and energy, potentially impacting any device traveling through the area of impact.