关键词: Boussinesq方程, 改进, 非线性, 色散性

Abstract: The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced
without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Padé (2,2) by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical
results obtained with the present model are in agreement with experimental data.

Key words: Boussinesq equation, improvement,nonlinearity, dispersion