In this paper, we investigate the non-linear loaded two-dimensional Benjamin-Ono equation by the functional variable method. The advantage of this method is reliability and efficiency. Using this method we obtained exact solitary and periodic wave solutions. The solving procedure is very simple and the traveling wave solutions of this equation are demonstrated by hyperbolic and trigonometric functions. The graphical representations of some obtained solutions are demonstrated to better understand their physical features.

In this article, we established new travelling wave solutions for the loaded Benjamin-Bona-Mahony and the loaded modified Benjamin-Bona-Mahony 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. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab program. We get some traveling wave solutions, which are expressed by the hyperbolic functions and trigonometric functions. This method is effective to find exact solutions of many other similar equations.

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In this article, we construct exact travelling wave solutions of the loaded modified Calogero-Degasperis equation by (G ′ /G) -expansion method. The efficiency of this method for finding these exact solutions has been demonstrated. We establish several classes of explicit solutions -hyperbolic and trigonometric solutions containing free parameters. The solitary wave solutions of this equation follow from the traveling wave solutions for certain values of the parameters. All calculations have been made with the aid of Matlab program. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

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