BOUSSINESQ TYPE EQUATIONS WITH FIRST ORDER OF NONLINEARITY AND FOURTH ORDER OF DISPERSION

In this paper, the Boussinesq-type equations with first-order O(α) of nonlinearity and fourth-order O(β 8) of dispersion is derived, in which, α=A/h 0 , β=h 0/L , A, L and h 0 is typical value of wave amplitude, wavelength and water depth By using the transforming velcity, the linear dispersion relation of our equations is consistent with fourth order pade approximation of the exact linear dispersion relation for Airy waves, this make the equations applicable to a wider rang...