A Camassa-Holm-Type Model For Shallow Water Waves With Surface Tension, Coriolis Effects, And Uneven Bottom

In this paper, we study the asymptotic behavior of the Green-Naghdi equations under the Camassa-Holm regime, incorporating uneven bottom topography, surface tension, and Coriolis effects. Using the Whitham modulation technique, we derive a modified CH-type equation for the new model. We construct explicit H s -consistent solutions with correctors up to order μ 2 , and establish H s -consistency for the corresponding asymptotic Green-Naghdi system. Finally, we provide numerical validation of the asymptotic expansion by evaluating the Green-Naghdi residuals along dynamically evolved CH solutions. The computed residuals exhibit quadratic scaling in μ, confirming second-order asymptotic consistency of the derived model.