Improved $\tan \left (\frac {\Phi (\xi )}{2}\right )$-Expansion Approach for Burgers Equation in Nonlinear Dynamical Model of Ion Acoustic Waves

Abstract

The main purpose of this research is to find new and more exact traveling wave solutions of nonlinear dynamical model of ion acoustic waves in plasma with the help of famous reductive perturbation technique. A well-known nonlinear evolution equation, namely Burgers equation, is derived to investigate ion acoustic waves in relativistic plasma containing electrons and positrons. The traveling wave solution of Burgers equation is carried out by an affective integration tool, namely improved $\tan \left (\frac {\Phi (\xi )}{2}\right )$ expansion method. As a result, different types of solutions such as periodic, kink, rational, exponential function, and hyperbolic function, are obtained. The wave profiles of solitary wave solutions are graphically depicted. The algorithm of the suggested technique is also outlined. It is admitted that the used method is efficient and influential tool for constructing solitary wave solutions of nonlinear evolution equations.