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December  2007, 6(4): 1043-1050. doi: 10.3934/cpaa.2007.6.1043

## Orbital stability of solitary waves of the Schrödinger-Boussinesq equation

 1 Faculty of Mathematics and Informatics, Shumen University, 9712 Shumen, Bulgaria

Received  February 2007 Revised  July 2007 Published  September 2007

This paper concerns the orbital stability of solitary waves of the Schrödinger-Boussinesq equation

$i\partial_t u+\partial_x^2 u+uv =0\qquad\qquad\qquad\qquad\qquad (0.1)$

$\partial_t^2 v-\partial_x^2 v+\partial_x^4 v+\partial_x^2 (3v^2+|u|^2)=0.$

By applying the abstract results of Grillakis, Shatah and Strauss [11, 12] and detailed spectral analysis developed by Lopes in [17], we obtain the stability of solitary waves.

Citation: Sevdzhan Hakkaev. Orbital stability of solitary waves of the Schrödinger-Boussinesq equation. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1043-1050. doi: 10.3934/cpaa.2007.6.1043
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