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Stability of solitary waves of a generalized Ostrovsky equation. (English) Zbl 1123.35056
The authors consider the stability problem of solitary wave solutions of a generalized Ostrovsky equation: \[ (u_t-\beta u_{xxx}+f(u)_x)_x=\gamma u, \;x\in \mathbb{R},\;\beta,\gamma =\text{consts.}, \] which is a modification of the Korteweg-de Vries equation widely used to describe the effect of rotation on surface and internal solitary waves or capillary waves. Using variational methods, the authors prove the existence of ground state solitary waves and show that such waves converge to solitary waves of the Korteweg-de Vries equation as the rotation parameter \(\gamma\) vanishes.
Reviewer: Ma Wen-Xiu (Tampa)

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
76B25 Solitary waves for incompressible inviscid fluids
58E30 Variational principles in infinite-dimensional spaces
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