Study of Langmuir waves for Zakharov equation using Sardar sub-equation method

The Zakharov equation is a nonlinear plasma fluid model, used for ion-acoustic waves in a magnetized plasma. In the present study, Langmuir waves of the dimensionless Zakharov equation are investigated by using the Sardar subequation method. The obtained solutions lead to a variety of exact solutions in the form of dark, bright, periodic singular, singular and combined dark-bright type solutions. These acquired solutions are depicted graphically by the 2D, contour and 3D plots which show the physical behaviour of obtained solutions. All the graphs confirm the validity of the obtained solutions. These types of solutions have a large range of applications in mathematical and applied sciences.