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

Document Type : Research Paper


1 Department of Mathematics, University of Okara, Okara, Pakistan

2 NED University of Engineering and Technology, Karachi, Pakistan

3 Department of Mathematics, University of the Punjab, Lahore, Pakistan


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.


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Volume 14, Issue 3
March 2023
Pages 9-18
  • Receive Date: 07 May 2022
  • Revise Date: 09 January 2023
  • Accept Date: 22 January 2023