The ion sound and Langmuir waves dynamical system via computational modified generalized exponential rational function

In this study, we investigate a system of equations based on ion sound and Langmuir waves equations using a generalized exponential rational function, and a new technique named as a modified generalized exponential rational function method. The concept of the new approach is to modify the generalized exponential rational function method. To evaluate the efficiency of the new scheme, we applied the two methods to the given system of equations, and we chose the same values of the parameters in all families, as well as we presented the difference between the solutions in the result and the discussion section. One might easily conclude that the new approach is quite effective and successful in seeking the exact solutions of the nonlinear differential equations . As a result, we have identified a variety of new families of exact travel wave solutions. In addition, we plotted 2D, 3D and contour graphs for some reported solutions by choosing the suitable parameters values. • We study modulation instability and wave soliton solutions. • We consider nonlinear evolution dynamical equations. • The ion sound and Langmuir waves equation is considered. • We applied hydrodynamic mathematical methods.