Relativistic effect on dust-acoustic waves and the associated rogue waves in Jupiter environment

To understand the nonlinear behavior of the dust acoustic solitary waves (DASWs) and the production of rogue waves (RWs) in the Jupiter environment at distances greater than 15 R J , a five-component relativistic dusty plasma system comprising positive dust particles, streaming positive ions, isothermal ions, electrons, and solar wind electrons has been considered. To analyze this system, the Korteweg-de Vries (KdV) equation is derived using the reductive perturbation method (RPM), and the nonlinear Schr & ouml;dinger equation (NLSE) is derived by employing the derivative expansion method. Both analytical and numerical (Adomian decomposition scheme) solutions of the KdV equation are studied. It is found that the nonlinearity and amplitude of dust-acoustic solitary waves (DASWs) as well as the width of the electric field structure increase, while the rogue wave (RW) amplitude decreases with the growing effect of the relativistic streaming positive ion factor. The analytic solution of the KdV equation provides only the rarefactive DASWs, while its numerical solution gives both compressive and rarefactive DASWs. This investigation may help not only to comprehend the space plasma phenomena, particularly in the Jupiter atmosphere, but also to validate laboratory investigations where concerned plasma species are present.