Study of compressive and rarefactive lump solitons structures in dusty plasma with double spectral (r,q) distributed electrons

Abstract

Nonlinear features are revealed by one of the most competent and powerful approaches, i.e. soliton theory. The present article starts with the dust collisionless magnetized plasma where electrons are following double spectral ( r , q ) distribution. From the hydrodynamical governing equations set, Kadomtsev–Petviashvili (KP) equation is derived using the reductive perturbation technique. The derived KP equations are converted to standard KP equations by a suitable transformation to use the Hirota bilinear method (HBM) more conveniently. By using HBM, an auxiliary function is constructed, and through symbolic computation, three arbitrary constant sets are formed. These sets associate with three lump soliton solution sets. Finally, all these lump soliton solutions are returned back by the inverse transformation that was used to make the derived KP equation to the standard KP equation and get the lump soliton solution of the associated system. It is investigated that associated plasma parameters have a significant impact on the lump soliton structures while tracing figures using these plasma parameters within the justified range of the system. While lump soliton features' are analysed for various parameters' effect on it, one most important aspect is revealed. Double spectral index r and q play a significant role in the lump solitons structures and depict compressive and rarefactive lump soliton structures with the associated system. It is found that these double spectral indices r and q are the decision-making parameters for the lump soliton structures to be compressive or rarefactive.