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Long‐time Solutions of the Ostrovsky Equation
Author(s) -
Grimshaw Roger,
Helfrich Karl
Publication year - 2008
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.1467-9590.2008.00412.x
Subject(s) - wavenumber , wave packet , nonlinear system , korteweg–de vries equation , physics , inertia , mathematical analysis , classical mechanics , mathematics , rotation (mathematics) , mathematical physics , quantum mechanics , geometry
The Ostrovsky equation is a modification of the Korteweg‐de Vries equation which takes account of the effects of background rotation. It is well known that the usual Korteweg‐de Vries solitary wave decays and is replaced by radiating inertia gravity waves. Here we show through numerical simulations that after a long‐time a localized wave packet emerges as a persistent and dominant feature. The wavenumber of the carrier wave is associated with that critical wavenumber where the underlying group velocity is a minimum (in absolute value). Based on this feature, we construct a weakly nonlinear theory leading to a higher‐order nonlinear Schrödinger equations in an attempt to describe the numerically found wave packets.