AM  Vol.2 No.8 , August 2011
Orbital Stability of Solitary Waves for Generalized Klein-Gordon-Schrodinger Equations
ABSTRACT
This paper concerns the orbital stability for exact solitary waves of the Generalized Klein-Gordon-Schrod-inger equations. Since the abstract results of Grillakis et al[1-2] can not be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves.

Cite this paper
nullW. Qi and G. Lin, "Orbital Stability of Solitary Waves for Generalized Klein-Gordon-Schrodinger Equations," Applied Mathematics, Vol. 2 No. 8, 2011, pp. 1005-1010. doi: 10.4236/am.2011.28139.
References
[1]   M .Grillakis, J. Shatah and W. Strauss, “Stability Theory of Solitary Waves in the Presence of Symmetry, Ⅰ,” Journal of Functional Analysis, Vol. 74, No. 1, 1987, pp. 160-197. doi:10.1016/0022-1236(87)90044-9

[2]   M. Grillakis, J. Shatah and W. Strauss, “Stability Theory of Solitary Waves in the Presence of Symmetry, Ⅱ,” Journal of Functional Analysis, Vol. 94, No. 2, 1990, pp. 308-348.

[3]   I. Fukuda and M. Tsumi, “On Coupled Klein-Gordon- Equations,” Journal of Applied Mathematics, Vol. 66, 1978, pp. 358-378.

[4]   J. P. Albert and J. L. Bona, “Total Positivity and the Stability of Internal Waves in Stratified Fluids of Finite Depth,” IMA Journal of Applied Mathematics, Vol. 46, No. 1-2, 1991, pp. 1-19. doi:10.1093/imamat/46.1-2.1

[5]   M. Reed and B. Simon, “Methods of Modern Mathematical Physics: Fourier Analysis, Self-Adjointness,” Academic Press, Waltham, 1975.

[6]   B. L. Guo and L. Chen, “Orbital Stability of Solitary Waves of the Long Wave-Short Wave Resonance Equations,” Mathematical Methods in the Applied Sciences, Vol. 21, No. 10, 1998, pp. 883-894.

 
 
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