Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the stability of solitary waves for the Ostrovsky equation


Author: Yue Liu
Journal: Quart. Appl. Math. 65 (2007), 571-589
MSC (2000): Primary 35Q53, 35B60, 76B25
DOI: https://doi.org/10.1090/S0033-569X-07-01065-8
Published electronically: July 26, 2007
MathSciNet review: 2354888
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Abstract: Considered herein is the stability of solitary-wave solutions of the Ostrovsky equation which is an adaptation of the Korteweg-de Vries equation widely used to describe the effect of rotation on the surface and internal solitary waves or the capillary waves. It is shown that the ground state solitary waves are global minimizers of energy functionals with the constrained variational problem and are deduced to be nonlinearly stable for the small effect of rotation. The analysis makes frequent use of the variational properties of the ground states.


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Additional Information

Yue Liu
Affiliation: Department of Mathematics, University of Texas, Arlington, Texas 76019
Email: yliu@uta.edu

DOI: https://doi.org/10.1090/S0033-569X-07-01065-8
Keywords: Ostrovsky equation, solitary waves, stability, weak rotation
Received by editor(s): November 20, 2006
Published electronically: July 26, 2007
Article copyright: © Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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