This article concerns with the construction of the analytical traveling wave solutions for the model of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave and the higher-order nonlinear Schrödinger equation by Riccati–Bernoulli sub-ODE method. We give the exact solutions for these two equations. The proposed method is effective tool to solve many other nonlinear partial differential equations. Moreover, this method can give a new infinite sequence of solutions. These solutions are expressed by hyperbolic, trigonometric and rational functions. Finally, with the aid of Matlab release 15, some graphical simulations were designed to see the behavior of these solutions.

The nonlinear Maccari's systems depict the dynamics of isolated waves, detained in a small part of space, in optical communications, hydrodynamics and plasma physics. In this paper, we construct some new solutions for the Maccari's systems, using the unified solver technique based on He's variations technique. These solutions prescribe some vital complex phenomena in plasma physics. The proposed solver will be used as a box solver for considering various models in applied science and new physics. Some graphs are presented in order to display the dynamical behaviour of the gained solutions.