The limit behavior of the solutions to a class of nonlinear dispersive wave equations

In this paper, we study the limit behavior of the solutions to a class of nonlinear dispersive wave equations. We also demonstrate that the solutions to Eq. (1.1) converge to the solution to the corresponding BBM equation as the parameter γ converges to zero. And the convergence of solutions to Eq. (1.1) as α2→0 is studied in Hs (R), s > 32 . Given the discussion of the parameters in the nonlinear dispersive wave equation (1.1), one will obtain some conditions in which compacton and peakon occur. © 2007 Elsevier Inc. All rights reserved