On the Exact Solitary Wave Solutions to the New ($2+1$) and ($3+1$)-Dimensional Extensions of the Benjamin-Ono Equations

Abstract

In this paper, the Kudryashov method to construct the new exact solitary wave solutions for the newly developed ( 2 + 1 )-dimensional Benjamin-Ono equation is successfully employed. In the same vein, also the new ( 2 + 1 )-dimensional Benjamin-Ono equation to ( 3 + 1 )-dimensional spaces is extended and then analyzed and investigated. Different forms of exact solitary wave solutions to this new equation were also determined. Graphical illustrations for certain solutions in both equations are provided. We alternatively offer that the determining method is general, impressive, outspoken, and powerful and can be exerted to create exact solutions of various kinds of nonlinear models originated in mathematical physics and engineering.