A novel analytical approach to the Benjamin–Ono equation

Abstract

This article examines some traveling wave solutions to the second-order Benjamin-Ono equation by using an analytical scheme via the sine-Gordon expansion technique. The Benjamin-Ono equation is similar to the KdV equation and it describes internal waves in fluids in a deep layer. We achieved some traveling wave solutions, including hyperbolic functions. All the obtained solutions were graphically analyzed based on their physical properties. As a result, the mentioned method is an effective one that provides analytical solutions for strongly non-linear partial differential models.