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

Abstract

AbstractIn 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