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The nonlinear propagation of dust-ion-acoustic shock waves (DIASWs) in unmagnetized dusty plasma comprising inertial ions, non-Maxwellian electrons with two distinct temperatures, and negatively charged dust is investigated in this article using a different approach based on the Sagdeev pseudopotential theory. The reductive perturbation approach is used to produce the KdVB and mKdVB equations and a comparison of their analytical and numerical solutions is shown. The effects of various parameters consisting of macroscopic non-thermal, ion-kinematic viscosity, etc. that significantly alternate the qualitative properties of DIASW are discussed. Both oscillatory and monotonic natures of the dispersive-diffusive shock wave structures are described in the present study. It has also been concentrated on nonlinear dynamics in such a plasma environment. The findings of this study should aid in understanding the nonlinear dynamics of wave damping and interactions in space and laboratory dusty plasmas, where the most relevant plasma parameters are kinematic viscosity and macroscopic non-thermality.

The propagation dynamics of the nucleus-acoustic waves (NAW) in a quantum plasma composed of nondegenerate inertial light nuclei, stationary heavy nuclei, and ultra-relativistically degenerate electrons and positrons has been theoretically investigated within the framework of the Boussinesq equation, which is valid for a bi-directional propagation of a small but finite amplitude limit. The N-soliton solution of the Boussinesq equation is derived using Hirota's method. It is found that positive potential structures exist in the sonic and supersonic regimes, whereas negative potential structures are found to be present in the subsonic regime. Pertinent plasma properties are analyzed for one-, two-, and three-soliton solutions in terms of different parameters. In addition to the typical solitary wave solutions, our findings indicate that the nonlinear NAW has breather structures. The three- and four-soliton solutions are used to construct the elastic interaction solutions of the breather–soliton and breather–breather, respectively. The findings are discussed in the context of ultra-relativistic astrophysical plasmas.

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