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In this work, we have looked into the amplitude modulation and formation of enveloping soliton in a dense plasma with thermal degeneracy pressure expressions as a strong laser beam falls on it. We have focused on the situation where an intense laser interacts with plasma and we have made use of a new topological treatment of problems containing a set of coupled differential equations. At first, we have solved the equations to arrive at the dispersion relation. We have studied phase plots using particle-in-cell (PIC) simulation from where Kelvin–Helmholtz-type instabilities were observed. We have made use of the homotopy perturbation technique to find out more about the evolution of density, electric field, velocity streamlines, and the subsequent amplitude modulation with different types of nonlinearity. We identified the range of plasma and laser parameters in which such nonlinearity is important. The results obtained here will help interpret different phenomena that arise in laser–plasma interaction and plasma astrophysics where shocks solitons, and so on in dense hot plasma can be studied in laboratory scales.

The dust-ion collisional effect is investigated for dust ion acoustic waves (DIAWs) in the spherical and cylindrical geometry. Using the reductive perturbation technique (RPT), the evolution equation is derived with an additional damping term. An approximate analytical time-dependent solitary wave solution is obtained for the evolution equation in nonplaner geometry. It is seen that dust ion collisional frequency plays an important role in the existence region of the solitary wave structure in the nonplanar geometry. It is also seen that dust-ion collisional frequency and spectral index $\kappa $ have a significant role in the amplitude and width of the solitary wave. Additionally, we have numerically investigated the parametric influence on the solitonic evolution mechanism which will help understand the process better.