Instability of solitary waves for a generalized Benney-Luke equation

Nonlinear Analysis, Theory, Methods and Applications

Volumn 68, Issue 10, 2008, Pages 3009-3033

  Quintero, José Raúl ^a   Muñoz Grajales, Juan Carlos ^a  

^a UNIVERSIDAD DEL VALLE   (Colombia)

Author keywords

Boussinesq equation; Eigenvalue problem; Linear instability; Solitary wave

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; LINEAR EQUATIONS; ONE DIMENSIONAL; SURFACE TENSION; WAVE PROPAGATION;

BENNEY-LUKE EQUATION; BOUSSINESQ EQUATION;

SOLITONS;

EID: 40849142442     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.02.042     Document Type: Article

References (23)

1. Alexander J., Gardner R., and Jones C.K.R.T. A topological invariant arising in the stability analysis of travelling waves. J. Reine Angew. Math. 410 (1990) 67-212
2. Benjamin T. The stability of solitary waves. Proc. R. Soc. Lond. A 328 (1972) 153-183
3. Bona J. On the stability of solitary waves. Proc. R. Soc. Lond. A 344 (1976) 363-374
4. Bona J., Souganidis P., and Strauss W. Stability and instability of solitary wave. Proc. R. Soc. Lond. A 411 (1987) 395-412
5. Evans J.W. Nerve axon equations. IV: The stable and unstable impulse. Indiana Univ. Math. J. 24 (1975) 1169-1190
6. Gohberg I.C., and Sigal E.I. An operator generalization of the logarithmic residue theorem and the theorem of Rouché. Mat. Issled. 13 4 (1971) 603-625
7. Gohberg I.C., Goldberg S., and Kaashoekand M.A. Classes of Linear Operators (1993), Springer-Verlag, New York
8. Grillakis M., Shatah J., and Strauss W. Stability theory of solitary waves in presence of symmetry, I. J. Funct. Anal. 74 (1987) 160-197
9. Jones C.K.R.T. Stability of travelling waves solutions to the FitzHugh-Hagumo equation. Trans. Amer. Math. Soc. 286 (1984) 431-469
10. Y.A. Li, The eigenvalue problem for solitary waves of the Green-Naghdi equations, in: Mathematical and Numerical Aspects of Wave Propagation (Santiago de Compostela, 2000), SIAM, Philadelphia, PA, 2000, pp. 339-343
11. Muñoz Grajales J.C., and Nachbin A. Dispersive wave attenuation due to orographic forcing. SIAM J. Appl. Math. 64 3 (2004) 977-1001
12. Muñoz Grajales J.C., and Nachbin A. Stiff microscale forcing and solitary wave refocusing. SIAM Multiscale Model. Simul. 3 3 (2005) 680-705
13. Nachbin A. A terrain-following Boussinesq system. SIAM J. Appl. Math. 63 3 (2003) 905-922
14. 2 and the Fourier transform. AMS 95 2 (1985) 252-254
15. Pego R., and Weinstein M. Eigenvalues, and instabilities of solitary waves. Philos. Trans. R. Soc. Lond., A 340 (1992) 47-94
16. Pego R., and Weinstein M. Asymptotic stabilities of solitary waves. Philos. Trans. R. Soc. Lond., A 340 (1994) 305-349
17. Pego R., and Weinstein M. Convective linear stability of solitary waves for Boussinesq equation. AMS 99 (1997) 311-375
18. R. Pego, J. Quintero, Asymptotic stability of solitary waves in the Benney-Luke model of water waves (2005) (in preparation)
19. Quintero J. Existence and analyticity solitary waves for a generalized Benney-Luke equation. Rev. Colombiana Mat. 36 (2002) 71-95
20. Quintero J. Nonlinear stability of a 2-D Benney-Luke equation. J. Discrete Cont. Dyn. Syst. 13 1 (2005) 203-218
21. Quintero J. Nonlinear stability of a one-dimensional Boussinesq equation. J. Dyn. Differential Equations 15 1 (2003) 125-142
22. Quintero J., and Arenas G. The eigenvalue problem for solitary waves of a Boussinesq equation, via a generalization of the Rouché theorem. J. Appl. Anal. 83 (2004) 1229-1244
23. Smereka P. A remark on the solitary waves stability for a Boussinesq equation. In: Debnath L. (Ed). Nonlinear Dispersive Wave Systems (1992), World Scientific, Singapore 255-263