Improvement of the Exp-function method for solving the BBM equation with time-dependent coefficients

In this article, we establish the exact solutions for the BBM equation with time-dependent coefficients. The Exp-function method (EFM) and improvement of the Exp-function method (IEFM) are used to construct solitary and soliton solutions of nonlinear evolution equations. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. The exact particular solutions are of four types: the hyperbolic function solution, trigonometric function solution, exponential solution and rational solution. It is shown that the EFM and IEFM, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.