A Functional Variable Method (FVM) Analytical Solution of the Benjamin-Ono Equation: Visual Methods for Wave Speed

Abstract

Numerous techniques have been used in mathematical physics to find precise solutions to a variety of nonlinear partial differential equations (NLPDEs). The Functional Variable Method (FVM) is a very effective solution method. In this paper, we achieve graphical representation for various parameters and discuss the validity and benefits of this method in the Benjamin-Ono equation. In the present paper, we solve the non-K-dv type equation, which is the Benjamin-Ono equation. This practical approach demonstrates that the FVM is more general and effective than the alternative. For different wave speeds, we displayed the soliton solutions graphically.