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The limit behavior of the solutions to a class of nonlinear dispersive wave equations |
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| Authors: | Lixin Tian Guilong Gui |
| Affiliation: | a Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Jiangsu 212013, PR China b Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu 212013, PR China c Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China |
| Abstract: | 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),  . 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. |
| Keywords: | Nonlinear dispersive wave equation Bi-Hamiltonian structure Well-posedness Weak and strong limit Peakon Compacton |
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