Abstract:
 The initial and boundaryvalue problem for the BenjaminBonaMahony (BBM)equation is studied in this paper. The goal is to understand the periodic behavior(termed as eventual periodicity) of its solutions corresponding to periodic boundary condition or periodic forcing. To this aim, we derive a new formula representing solutions of this initial and boundaryvalue problem by inverting the operator $\partial_t +\alpha \partial_x \gamma\partial_{xxt}$
defined in the spacetime quarter plane. The eventual periodicity of the linearized BBM equation with periodic boundary data and forcing term is established by combining this new representation formula and the method of stationary phase.
