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Soliton and Periodic Wave Solutions of the Nonlinear Loaded (3+1)-Dimensional Version of the Benjamin-Ono Equation by Functional Variable Method
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KeyWord:Nonlinear loaded Benjamin-Ono equation, solitary wave solutions, functional variable method, nonlinear evolution equations, periodic wave solutions, trigonometric function, hyperbolic function
Author NameAffiliation
Bazar Babajanov Doctor of Sciences in Physical and Mathematical Sciences, Department of Applied Mathematics and Mathematical Physics, Urgench State University, 220100, Urgench, Uzbekistan 
Fakhriddin Abdikarimov Phd student, Khorezm Mamun Academy, 220900, Khiva, Uzbekistan 
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      In this article, we establish new travelling wave solutions for the nonlinear loaded (3+1)-dimensional version of the Benjamin-Ono equation by the functional variable method. The performance of this method is reliable and effective and the method provides the exact solitary wave solutions and periodic wave solutions. The solution procedure is very simple and the traveling wave solutions are expressed by hyperbolic functions and trigonometric functions. After visualizing the graphs of the soliton solutions and the periodic wave solutions, the use of distinct values of random parameters is demonstrated to better understand their physical features. It has been shown that the method provides a very effective and powerful mathematical tool for solving nonlinear equations in mathematical physics.