References
- Bona JL, Sachs RL. Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation. Comm. Math. Phys. 1988;118:15–29.
- Linares F. Global existence of small solutions for a generalized Boussinesq equation. J. Differ. Equ. 1993;106:257–293.
- Liu Y. Instability and blow-up of solutions to a generalized Boussinesq equation. SIAM J. Math. Anal. 1995;26:1527–1546.
- Liu YC, Xu RZ. Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation. Physica D. 2008;237:721–731.
- Lin Q, Wu YH, Loxton R. On the Cauchy problem for a generalized Boussinesq equation. J. Math. Anal. Appl. 2009;353:186–195.
- Yang ZJ, Guo BL. Cauchy problem for the multi-dimensional Boussinesq type equation. J. Math. Anal. Appl. 2008;340:64–80.
- Zabusky NJ. Nonlinear partial differential equations. New York (NY): Academic Press; 1967.
- Boussinesq MJ. Essai sur la théorie des eaux courantes. Mém. Pésentés Divers Savants Acad. Sci. Inst. France. 1877;23:1–680.
- Kano T, Nishida T. A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves. Osaka J. Math. 1986;23:389–413.
- Makhankov VG. Dynamics of classical solitons (in non-integrable systems). Phys. Rep. 1978;35:1–128.
- Wang SB, Chen GW. Small amplitude solutions of the generalized IMBq equation. J. Math. Anal. Appl. 2002;264:846–866.
- Wang SB, Chen GW. The Cauchy problem for the generalized IMBq equation in Ws,p(Rn). J. Math. Anal. Appl. 2002;266:38–54.
- Clarkson A, Leveque RJ, Saxton R. Solitary-wave interactions in elastic rods. Stud. Appl. Math. 1986;75:95–122.
- Liu YC, Xu RZ. Potential well method for Cauchy problem of generalized double dispersion equations. J. Math. Anal. Appl. 2008;338:1169–1187.
- Xu RZ, Liu YC. Global existence and nonexistence of solution for Cauchy problem of multidimensional double dispersion equations. J. Math. Anal. Appl. 2009;359:739–751.
- Wang SB, Chen GW. Cauchy problem of the generalized double dispersion equation. Nonlinear Anal. 2006;64:159–173.
- Chen GW, Wang YP, Wang SB. Initial boundary value problem of the generalized cubic double dispersion equation. J. Math. Anal. Appl. 2004;299:563–577.
- Polat N, Ertas A. Existence and blow-up of solution of Cauchy problem for the generalized damped multidimensional Boussinesq equation. J. Math. Anal. Appl. 2009;349:10–20.
- Xu RZ, Liu YC, Yu T. Global existence of solution for Cauchy problem of multidimentional generelized double dispersion equations. Nonlinear Anal. 2009;71:4977–4983.
- Wang S, Da F. On the asymptotic behavior of solution for the generalized double dispersion equation. Appl. Anal. 2012; http://dx.doi.org/10.1080/00036811.2012.661044.
- Schneider G, Wayne CE. Kawahara dynamics in dispersive media. Physica D. 2001;152–153:384–394.
- Xia S, Yuan J. Existence and scattering of small solutions to a Boussinesq type equation of six order. Nonlinear Anal. 2010;73:1015–1027.
- Wang HW, Wang SB. Global existence and asymptotic behavior of solution for the Rosenau equation with hydrodynamical damped term. J. Math. Anal. Appl. 2013;401:763–773.
- Pişkin E, Polat N. Existence, nonexistence and asymptotic behavior of solutions for Cauchy problem of multidimensional generalized damped Boussinesq-type equation. Turk. J. Math. 2014;38:706–727.
- Levine HA. Instability and nonexistence of global solutions to nonlinear wave equations of the form Putt = − Au + F(u). Trans. Amer. Math. Soc. 1974;192:1–21.
- Levine HA, Sleeman BD. A note on the non-existence of global solutions of initial boundary value problems for the Boussinesq equation utt = 3uxxxx + uxx − 12(u2)xx. J. Math. Anal. Appl. 1985;107:206–210.
- Clements J. Existence theorems for a quasi-linear evolution equation. SIAM J. Appl. Math. 1974;26:745–752.