Abstract
In the present study a simplified phenomenological model of shallow-water wave propagating mainly in the equatorial ocean regions with the Coriolis effect caused by the Earth’s rotation is formally derived. The model equation which is analogous to the Green–Naghdi equations with the second-order approximation of the Camassa–Holm scaling captures stronger nonlinear effects than the classical dispersive integrable equations like the Korteweg–de Vries and two-component Camassa–Holm system. The local well-posedness of the Cauchy problem is then established by the linear transport theory and wave-breaking phenomenon is investigated based on the method of characteristics and the Riccati-type differential inequality. Finally, the condition of permanent waves is demonstrated by analyzing competition between the slope of average of horizontal velocity component and the free surface component.
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