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The Exact Solutions for the Benjamin-Bona-Mahony Equation
  
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KeyWord:Generalized hyperbolic tangent function method; The modified hyperbolic function expanding method; Traveling wave solution; Balance coefficient method; Partial differential equation
Author NameAffiliation
Xiaofang Duan School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China
School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710126, China 
Junliang Lu School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
Yaping Ren School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
Rui Ma School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China 
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Abstract:
      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.