Abstract
In this work, we consider the propagation of one-dimensional nonlinear unmagnetized dusty plasma, by using the reductive perturbation technique to formulate the nonlinear mathematical model which is further modified Korteweg-de Vries (fmKdV) dynamical equation. We use the extend form of two methods, auxiliary equation mapping and direct algebraic methods, to investigate the families of dust and ion solitary wave solutions of one-dimensional nonlinear fmKdV. These new exact and solitary wave solutions, which represent the electrostatic potential and pressure for fmKdV, and also the graphical representation of electrostatic potential and pressure are shown with the aid of Mathematica.