New soliton solutions of ion dynamics on acoustic dusty plasma

This paper discusses the newly discovered acoustic waves that arise from the equilibrium between the inertia of dust particles and plasma pressure. The propagation of these waves is demonstrated to be non-linear, with supersonic solitons exhibiting either a positive or negative electrostatic potential, and linear, with normal modes in a dusty plasma. Implementing the unified method and the generalized projective Ricatti equation technique, we generate a variety of optical wave structures for the governing framework. Using 3 D and 2 D dimensional illustrations, the fundamental behavior of the derived solutions is visually analyzed by choosing appropriate values for arbitrary parameters that satisfy the specified constraints. The employed methodologies are acknowledged to be a powerful and effective mechanism for creating solitary wave solutions for non-linear evolution models.