American Institute of Mathematical Sciences

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June  2007, 7(4): 793-806. doi: 10.3934/dcdsb.2007.7.793

Stability and weak rotation limit of solitary waves of the Ostrovsky equation

Steve Levandosky 1, and  Yue Liu 2,

1. 

Mathematics and Computer Science Department, College of the Holy Cross, Worcester, MA, 01610, United States
2. 

Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408

Received  March 2006 Revised  January 2007 Published  March 2007

In this paper we study several aspects of solitary wave solutions of the Ostrovsky equation. Using variational methods, we show that as the rotation parameter goes to zero, ground state solitary waves of the Ostrovsky equation converge to solitary waves of the Korteweg-deVries equation. We also investigate the properties of the function $d(c)$ which determines the stability of the ground states. Using an important scaling identity, together with numerical approximations of the solitary waves, we are able to numerically approximate $d(c)$. These calculations suggest that $d$ is convex everywhere, and therefore all ground state solitary waves of the Ostrovsky equation are stable.
Keywords: solitary waves, stability, KdV-like equations, variational principles..
Mathematics Subject Classification: Primary: 35Q53, 76B25, 58F10; Secondary: 58E3.
Citation: Steve Levandosky, Yue Liu. Stability and weak rotation limit of solitary waves of the Ostrovsky equation. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 793-806. doi: 10.3934/dcdsb.2007.7.793
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