The reduced Ostrovsky equation : integrability and breaking
Grimshaw, Roger H. J.
Helfrich, Karl R.
Johnson, Edward R.
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The reduced Ostrovsky equation is a modi cation of the Korteweg-de Vries equation, in which the usual linear dispersive term with a third-order deriva- tive is replaced by a linear non-local integral term, which represents the e ect of background rotation. This equation is integrable provided a certain curvature constraint is satis ed. We demonstrate, through theoretical analysis and numeri- cal simulations, that when this curvature constraint is not satisfi ed at the initial time, then wave breaking inevitably occurs.
Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of Massachusetts Institute of Technology for personal use, not for redistribution. The definitive version was published in Studies in Applied Mathematics 129 (2012): 414–436, doi:10.1111/j.1467-9590.2012.00560.x.