Role of adiabatic pressure on dust kinetic Alfvén solitary waves in an electron-depleted dusty magnetized plasma

Kinetic Alfvén waves (KAWs) are fundamental low-frequency electromagnetic modes in magnetized plasmas, playing a crucial role in energy transfer and wave–particle interactions. Their dynamics are significantly influenced by the adiabatic pressure, which arises from the thermal motion of plasma particles and is further modified by the presence of charged dust grains. This study investigates the nonlinear behavior of KAWs in an electron-depleted (which describes that dust particles capture nearly all free electrons, dramatically reducing electron density and amplifying the influence of ions and dust grains) magnetized plasma featuring nonextensive two-temperature ion distributions and the impact of negatively charged dust-induced adiabatic pressure. Using the reductive perturbation method, we derive the Korteweg–de Vries (KDV) and modified KDV (MKDV) equations to describe the propagation of KAWs. Our analysis reveals that the nonextensive distribution significantly alters the wave’s nonlinear properties, while the two-temperature ion model introduces additional complexities to wave behavior. Moreover, the presence of dust enhances the thermal pressure, affecting both the propagation and stability of the waves and leading to the emergence of dust KAWs. We demonstrate that the KDV solitary amplitude is not affected by adiabatic pressure; however, its influence is apparent in the amplitude when higher-order nonlinearities (i.e., the MKDV equation) are taken into account. These findings provide deeper insights into nonlinear phenomena in space plasmas, with significant implications for astrophysical research.