Construction of solitary wave solutions to the nonlinear modified Kortewege-de Vries dynamical equation in unmagnetized plasma via mathematical methods

In this research, we consider the propagation of one-dimensional nonlinear behavior in a unmagnetized plasma. By using the reductive perturbation technique to formulate the nonlinear mathematic model which is modified Kortewege-de Vries (mKdV), we apply the extended form of two methods, which are extended auxiliary equation mapping and extended direct algebraic methods, to investigate the new families of electron-acoustic solitary wave solutions of mKdV. These new exact traveling and solitary wave solutions which represent the electrostatic potential for mKdV and also the graphical representation of electrostatic potential are shown with the aid of Mathematica.