A new parabolic equation for propagation of weakly nonlinear Stokes waves over uneven bottom

Considering the limitation of mild-slope equation, requiring a computational effort and the mild-slope assumption, in practical engineering, a new nonlinear parabolic equation including the second-order long-waves ignored in the previous like equation is obtained by way of the parabolic approximation on Liu and Dingemans's third order evolution equation for Stokes waves propagating over uneven bottom applicable to mild and abrupt topography.The model theory can provide more accurate predictions by comparison of the numerical model results with the classic experimental data of Berkhoff et al.