Abstract
The anomalous Ostrovsky equation, which describes waves in vertically sheared ocean flows and magnetoacoustic waves, possesses steadily propagating, finite-amplitude, localized wave-packet solutions. It is shown here that these solutions can be obtained asymptotically, using Whitham modulation theory, as the solution to a nonlinear eigenvalue problem. This allows the various wave-packet solutions to be delineated and compared to solutions of the full equations of motion. A periodic solution with an embedded wave train is also constructed.
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