Constructions of new abundant traveling wave solutions for system of the ion sound and Langmuir waves by the variational direct method

In this paper, a novel and simple approach called the variational direct method (VDM) is applied to construct the exact traveling wave solutions of the system of ion sound and Langmuir waves (SEISLWs), which is under the influence of the ponderomotive force caused by a nonlinear force experienced by a charged particle in an inhomogeneous oscillating electromagnetic field due to high-frequency field. These exact solutions include the bright soliton, bright-like soliton, kinky-bright soliton, bright-dark soliton and periodic wave solutions, which are all presented through the numerical results in the form of 3-D plots. Obtained results show that the VDM is simple, straightforward and powerful, which is expected to open new perspectives for the traveling wave theory.