Solitary and periodic wave solutions of the loaded Boussinesq and the loaded modified Boussinesq equation

In this article, we establish new traveling wave solutions for the loaded Boussinesq equation and the loaded modified Boussinesq equation by the functional variable method. The performance of this method is reliable and effective and gives the exact solitary wave solutions and periodic wave solutions of the loaded Boussinesq equation and its modifications. The traveling wave solutions obtained via this method are expressed by hyperbolic functions and the trigonometric functions. The graphical representations of some obtained solutions are demonstrated to better understand their physical features, including bell-shaped solitary wave solutions, singular soliton solutions and solitary wave solutions of kink type. This method presents a wider applicability for handling nonlinear wave equations.

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