Dispersive Nonlinear Shallow‐Water Equations

A set of dispersive and hyperbolic depth‐averaged equations is obtained using a hyperbolic approximation of a chosen set of fully nonlinear and weakly dispersive Boussinesq‐type equations. These equations provide, at a reasonably reduced cost, both a physically sound description of the nearshore dynamics and a complete representation of dispersive and nonlinear wave phenomena. A detailed description of the conditioning of the dispersive terms and a physical interpretation of the hyperbolic approximation is provided. The dispersive and hyperbolic structure of the new set of equations is analyzed in depth and an analytical solitary‐wave solution is found.