Damping Effects on the Spectrum of Solitary Structures in Cylindrical and Spherical Geometry

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.