Higher-order shock wave structures and phase plane analysis in multicomponent dusty plasma

In this investigation, dust acoustic (DA) shocks and dressed shocks formed due to the contribution of higher-order effects in a non-Maxwellian plasma have been examined. The reductive perturbation method is employed to derive the nonlinear Burgers and Burgers-type inhomogeneous equations with the contribution of higher-order effects of nonlinearity and dissipation. The properties of dust acoustic shocks and higher order (dressed shocks) are examined from the solutions of these nonlinear equations under the effect of various plasma parameters. Furthermore, the travelling wave analysis is used to obtain the dynamical system for the Burgers equation using bifurcation theory. The characteristic properties of DA periodic waves have also been analysed under the influence of various plasma parameters.