Novel solitary wave solution in shallow water and ion acoustic plasma waves in-terms of two nonlinear models via MSE method

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By using modified simple equation method, we study the generalized RLW equation and symmetric RLW equation, the subsistence of solitary wave, periodic cusp wave, periodic bell wave solutions are obtained. We establish some conditions on the parameters for which the obtained solutions are dark or bright soliton. The proficiency of the methods for constructing exact solutions has been established. Finally, the variety of structure and graphical representation makes the dynamics of the equations visible and provides the mathematical foundation in shallow water, plasma and ion acoustic plasma waves.