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The Reduced Ostrovsky Equation: Integrability and Breaking
Author(s) -
Grimshaw R. H. J.,
Helfrich Karl,
Johnson E. R.
Publication year - 2012
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2012.00560.x
Subject(s) - integrable system , curvature , mathematics , constraint (computer aided design) , term (time) , mathematical analysis , rotation (mathematics) , mathematical physics , physics , geometry , quantum mechanics
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.