Solitary and periodic wave solutions of the loaded modified Benjamin-Bona-Mahony equation via the functional variable method

B. Babajanov (Urgench State University),
F. Abdikarimov (Khorezm Mamun Academy),


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.


loaded Benjamin-Bona-Mahony equation; loaded modified Benjamin-Bona-Mahony equation; hyperbolic functions; trigonometric functions; periodic wave solutions; solitary wave solutions; functional variable method

MSC 2020

34A34; 34B15; 35Q51; 35J60; 35J66

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