The Exact Solutions for the Benjamin-Bona-Mahony Equation (Journal of Nonlinear Modeling and Analysis, 2024)
The Benjamin-Bona-Mahony (BBM) equation represents the unidirectional propagation of nonlinear dispersive long waves, which has a clearphysical background, and is a more suitable mathematical and physical equation than the KdV equation. Therefore, the research on the BBM equationis very important. In this article, we put forward an effective algorithm, themodified hyperbolic function expanding method, to build the solutions of theBBM equation. We, by utilizing the modified hyperbolic function expandingmethod, obtain the traveling wave solutions of the BBM equation. When theparameters are taken as special values, the solitary waves are also derived fromthe traveling waves. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. Themodified hyperbolic function expanding method is direct, concise, elementaryand effective, and can be used for many other nonlinear partial differentialequations.