Homotopy analysis method for generalized Benjamin-Bona-Mahony equation

An analytic technique, the homotopy analysis method (HAM), is applied to solve the generalized Benjamin{Bona{Mahony (BBM) equation. An explicit series solution is given, di®erent from traditional analytic techniques, our approach is independent of knowing some parameters. This analytic method provides us with a new way to obtain series solutions of such problems. The homotopy analysis method contains the auxiliary parameter ~, which provides us with a simple way to adjust and control the convergence region of series solution.

Benjamin{Bona{Mahony (BBM) equation; homotopy analysis method; regularized long-wave equation; modi¯ed BBM equation.