Homotopy perturbation method for studying dissipative nonplanar solitons in an electronegative complex plasma

The characteristic behavior of dissipative nonplanar (cylidrical and spherical) solitons in a collisional electronegative complex plasma consisting of inertia cold positive ion and inertialess Maxwellian negative ion and electron in addition to immoble negatively charged dust grains are investigated. Motivated by the laboratory experiment of Ghim and Hershkowitz [Y. Ghim (Kim) and N. Hershkowitz, Appl. Phys. Lett. 94, 151503 (2009)], the nonplanar hydrodynamic equations of the present plasma model are reduced to the damped nonplanar Korteweg-de Vries (dnKdV) equation using the reductive perturbation method (RPM). This equation is used to investigate the characteristics and dynamics of dissipative nonplanar solitons in a collisional electronegative dusty plasma. It is known that the dnKdV equation does not admit analytical solution due to the linear term (the ion-neutral collision term and the geometrical term). Thus, one of the most effective numerical methods will be used to find the dissipative nonplanar soliton solution for this equation. The numerical method used in our analysis called the homotopy perturbation method (HPM). The analytical solution of KdV equation in the absence of the linear term of the dnkdv equation is used in our numerical analysis as an initial condition/solution and the boundary conditions are identified precisely. The numerical results showed that this method is more stable, convergent, and easier than other numerical methods. In addition, this method reaches to the exact solution within a few iterations. The influence of damping term and relevant plasma configuration parameters on the soliton profile is reported.