The homogeneous balance method and its application to the Benjamin–Bona–Mahoney (BBM) equation

We make use of the homogeneous balance method and symbolic computation to construct new exact traveling wave solutions for the Benjamin–Bona–Mahoney (BBM) equation. Many new exact traveling wave solutions are successfully obtained, which contain rational and periodic-like solutions. This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations.