Nonlinear propagation of ion plasma waves in dust-ion plasma including quantum-relativistic effect

In this paper we have theoretically investigated the quantum and relativistic effects on ion plasma wave in an unmagnetised dust-ion plasma. By using the method of normal mode analysis, we have obtained a linear dispersion relation. It has been analysed numerically for quantum and relativistic effects on the propagation of ion plasma wave. By using the standard reductive perturbation technique, we have derived a Korteweg–de Vries (KdV) equation which describes the nonlinear propagation of the wave. Numerically, it is shown that only compressive type of soliton can exist in the plasma under consideration. It is found that the solitary wave profile depends significantly on the quantum and relativistic parameters. The dust size, dust charge and the dust number density are also shown to have significant influences on these solitary waves. The results of this present investigation have some relevance to the nonlinear propagation of ion plasma wave in some astrophysical, space and laboratory plasma environments.