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.