Abstract: Boussinesq type equations, can be used to simulate the nonlinear transformation of surface waves due to the effects of shoaling, refraction, diffraction, reflection and nonlinear action so on. Different linear dispersion charateristics can be obtained by different vertically integrated methods. A new form of the Boussinesq equations is derived by using two different layers the horizontal velocity variable. The 4th order of Pade approximation, that is exact linear dispersion relation of Airy waves, is obta...