An extended form of Boussinesq-type equations for nonlinear water waves

An extended form of Boussinesq-type equations with improved nonlinearity is presented for the water wave propagation and transformation in coastal areas. To improve the nonlinearity of lower order Boussinesq-type equations, without including higher order derivative terms, an extended form of Boussinesq-type equations is derived by a generalized method. The Stokes-type analysis of the extended equations shows that the accuracy of the second order and third order nonlinear characteristics is improved greatly. The numerical test is also carried out to investigate the practical performance of the new equations under different wave conditions. Better agreement with experimental data is found in the regions of strong nonlinear wave-wave interaction and harmonic generation.