Beyond the Burgers paradigm: the stabilizing role of higher-order nonlinearities in magnetized heavy ion-acoustic shocks

Abstract This paper investigates the role of higher-order nonlinearities in the propagation of heavy ion-acoustic shock waves (HIASWs) within a magnetized, collisionless plasma comprising inertial heavy ions and kappa-distributed electrons and positrons. Employing a reductive perturbation technique, we derive a magnetized Burgers equation governing the first-order electrostatic potential, alongside an extended, linearly inhomogeneous Burgers-type equation that encapsulating significantly higher-order corrections. Analytical stationary solutions for both the wave potential and the associated electric field are obtained. A comprehensive parametric analysis reveals that the fundamental properties of the shock waves, including phase velocity, amplitude, and width, are critically sensitive to the plasma parameters. A key finding is the identification of a substantial moderating influence from the higher-order terms, which manifest as a negative contribution to the total wave potential and introduce a complex, opposing structure to the electric field. This effect acts as a stabilizing mechanism, mitigating nonlinear wave steepening and refining the shock profile. The results provide a more robust framework for understanding the dynamics of nonlinear coherent structures in astrophysical and laboratory plasmas where non-Maxwellian, multicomponent environments are prevalent, underscoring the necessity of incorporating higher-order effects for accurate physical description.