The modified benjamin-bona-mahony equation via the extended generalized riccati equation mapping method

Abstract

The generalized Riccati equation mapping is extended together with the (G'/G) -expansion method and is a powerful mathematical tool for solving nonlinear partial differential equations. In this article, we construct twenty seven new exact traveling wave solutions including solitons and periodic solutions of the modified Benjamin-Bona-Mahony equation by applying the extended generalized Riccati equation mapping method. In this method, G'(μ) = p + rG(μ) + sG 2 (μ) is implemented as the auxiliary equation, where r, s and p are arbitrary constants and called the generalized Riccati equation. The obtained solutions are described in four different families including the hyperbolic functions, the trigonometric functions and the rational functions. In addition, it is worth mentioning that one of newly obtained solutions is identical for a special case with already published result which validates our other solutions.