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The Reduced Ostrovsky Equation: Integrability and Breaking

Authors


R. H. J. Grimshaw, Department of Mathematical Sciences, Loughborough University, U.K.; e-mail: R.H.J.Grimshaw@lboro.ac.uk

Abstract

The reduced Ostrovsky equation is a modification of the Korteweg-de Vries equation, in which the usual linear dispersive term with a third-order derivative is replaced by a linear nonlocal integral term, which represents the effect of background rotation. This equation is integrable provided a certain curvature constraint is satisfied. We demonstrate, through theoretical analysis and numerical simulations, that when this curvature constraint is not satisfied at the initial time, then wave breaking inevitably occurs.

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