Sagdeev potential and kinetic Alfvén solitons for dust acoustic wave in Saturn's magnetosphere

The dust kinetic Alfvén wave is examined in a plasma made up of negatively charged dust grains, superthermal electrons, and ions. The Korteweg–de Vries (KdV) equation is derived for nonlinear dust kinetic Alfvén waves (DKAWs) in a low-β framework using the reductive perturbation technique (RPM). The normalization approach described in Hasegawa and Mima [Phys. Rev. Lett. 37, 690 (1976)] is utilized to derive the KdV equation. The KdV equation is then turned into the Sagdeev potential energy integral equation. Kinetic Alfvén waves (KAWs) and the formation of possible solitons with both KdV and Sagdeev potential approach are illustrated with suitable plasma parameters of Saturn's F-ring. The investigation on how obliqueness of propagation (θ), superthermal indices κi (for ions) and κe (for electrons), and dust concentration (f) affect the shape and size of DKASWs, is carried. Only negative potential (rarefactive) structures are seen here. It is concluded that any plasma parameter that is going to modify its effective Debye length will always modify the structure profile of both Sagdeev potential curves and the corresponding profile of solitons. This investigation could help us comprehend the creation of nonlinear structures in space plasma especially Saturn's F-ring.