Conservation Laws and Travelling Wave Solutions for System of Ion Sound and Langmuir Waves

In this paper, system of equations for ion sound and Langmuir waves (ISLWs) is studied to construct novel exact solutions of the coupled nonlinear system. The extended F-expansion method is applied to get exact solutions of ISLWs model. These solutions include many different expressions in hyperbolic, trigonometric, rational and Jacobi elliptic function solutions, dark and bright solitary wave solutions. Geometrical shape for some of the obtained results are plotted under the selection of proper parameters. Furthermore, we employed the Lie point symmetry to investigate the conservation laws for the system.