Exact traveling wave solutions for the system of the ion sound and Langmuir waves by using three effective methods

This paper gives a study to the system of ion sound and Langmuir waves (SEISLWs). Seven sets of the traveling wave solutions (TWSs) like the bright solitary (Type-1, Type-2, Type-3, Type-4), kinky bright solitary, dark solitary and periodic wave solutions are developed through three effective methods, which are simplified extended tanh-function method, He’s frequency formulation and the energy balance theory. The dynamic behaviors of the absolute, real and imaginary parts of the solutions are also plotted via the 3-D contours. The results in this work fully prove that the proposed methods are powerful tools to construct abundant TWS for the PDEs arising in physics.