TY - JOUR
T1 - The Exact Solutions for the Benjamin-Bona-Mahony Equation
AU - Duan , Xiaofang
AU - Lu , Junliang
AU - Ren , Yaping
AU - Ma , Rui
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 628
EP - 649
PY - 2023
DA - 2023/08
SN - 4
DO - http://doi.org/10.12150/jnma.2022.628
UR - https://global-sci.org/intro/article_detail/jnma/21902.html
KW - Generalized hyperbolic tangent function method, The modified
hyperbolic function expanding method, Traveling wave solution, Balance coefficient method, Partial differential equation.
AB - <p style="text-align: justify;">The Benjamin-Bona-Mahony (BBM) equation represents the unidirectional propagation of nonlinear dispersive long waves, which has a clear
physical background, and is a more suitable mathematical and physical equation than the KdV equation. Therefore, the research on the BBM equation
is very important. In this article, we put forward an effective algorithm, the
modified hyperbolic function expanding method, to build the solutions of the
BBM equation. We, by utilizing the modified hyperbolic function expanding
method, obtain the traveling wave solutions of the BBM equation. When the
parameters are taken as special values, the solitary waves are also derived from
the traveling waves. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The
modified hyperbolic function expanding method is direct, concise, elementary
and effective, and can be used for many other nonlinear partial differential
equations.</p>