Orbital Stability of Solitary Waves for Generalized Klein-Gordon-Schrodinger Equations

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DOI: 10.4236/am.2011.28139   PDF   HTML     4,926 Downloads   8,582 Views   Citations

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.

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W. 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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[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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