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

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  • 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.
    Mathematics Subject Classification: Primary: 35Q53, 76B25, 58F10; Secondary: 58E30.

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