Orbital stability  of solitary waves of the Schrödinger-Boussinesq equation

Sevdzhan Hakkaev

doi:10.3934/cpaa.2007.6.1043

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2007, Volume 6, Issue 4: 1043-1050. Doi: 10.3934/cpaa.2007.6.1043

This issue Previous Article Global well-posedness for the $L^2$ critical nonlinear Schrödinger equation in higher dimensions Next Article $L^1$-estimates for the higher-order derivatives of solutions to parabolic equations subject to initial values of bounded total variation

Orbital stability of solitary waves of the Schrödinger-Boussinesq equation

Sevdzhan Hakkaev^1,

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

Received: February 2007

Revised: July 2007

Published: December 2007

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: 35Q55, 35B35, 37K45.

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