The bifurcation and exact travelling wave solutions for the modified Benjamin–Bona–Mahoney (mBBM) equation

By using methods from dynamical systems theory, this paper researches the bifurcation and exact travelling wave solutions for the modified Benjamin–Bona–Mahoney (mBBM) equation. Implicit exact parametric representations of all travelling wave solutions as well as some explicit analytic solutions are given. Specially, breaking wave solutions are obtained, which KdV equation does not include.

► We research the mBBM equation by using dynamic system method.
► The bifurcation of all travelling wave solutions is given.
► Four types of new exact travelling wave solutions are obtained.