Long‐time Solutions of the Ostrovsky Equation

Source abstract

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.