Generating New Hyperbolic Solutions for Nonlinear Physical Model by Tanh Method

Abstract

Tanh method is used in this paper to find hyperbolic solutions to ion sound and Langmuir wave systems describes ion sound wave and the Langmuir wave as part of the action of the ponder motive force caused by a high-frequency field. A power series in tanh method was used as an ansatz to obtain analytical solutions for certain nonlinear evolution equations of traveling wave type. The suggested method, is a powerful solution method and it based on wave transformation, converts the partial derivatives in the equation to ordinary derivatives and then generate new hyperbolic solutions to the system under consideration in this paper. Graphical simulations are introduced for some solutions. The method's main aspects will be discussed and the results showed the strength this using method through the new solutions obtained using tanh method. This method generates entirely new solutions for other types of nonlinear evolution equations observed in physics.