Burgers equation with cubic and quartic nonlinearity: dynamics of heavy ion-acoustic coherent structures in unmagnetized strongly coupled plasma

Abstract This study investigates the effects of plasma parameters on shock and periodic waves, along with their dynamic behaviors, in unmagnetized strongly coupled plasmas (SCPs), particularly with the presence of super-critical values (SCVs). To achieve this, the research extends the Burgers equation (BE) by incorporating higher-order nonlinear terms to explore the nonlinear characteristics of heavy ion acoustic (HIA) shock waves and periodic waves, along with their dynamics in SCPs. First, a BE with quartic nonlinearity is derived, which is used to analyze the propagation features of HIA shock waves near and at critical values (CVs) and SCVs. Based on the analytical solutions, the effects of plasma parameters on electrostatic shocks, anti-shocks, and their dynamic behaviors are examined. Second, the study investigates the propagation features of shock and periodic waves and their dynamics, not only near but also at SCVs, by deriving a new nonlinear evolution equation that incorporates both cubic and quartic nonlinearities. Since integrable nonlinear evolution equations are often solvable analytically, the research also assesses the need for numerical methods in studying acoustic wave phenomena in such plasmas. This approach provides a comprehensive understanding of both the theoretical and practical aspects of wave propagation in SCPs. The findings of this study may aid in understanding and predicting the behavior of HIA wave dynamics in space environments, such as stellar polytropes, hadronic matter, quark-gluon plasma, dark-matter halos, and contribute to future experimental studies in plasma laboratories.