An extended Boussinesq equation that models weakly nonlinear and weakly dispersive waves on a uniform layer of water is studied in this paper. The results show that the equation is not Painleveintegrable in general. Some particular exact travelling wave solutions are obtained by using a function expansion method. An approximate solitary wave solution with physical significance is obtained by using a perturbation method. We find that the extended Boussinesq equation with a depth parameter of 1√2 is able to match the Laitone＇s （1960） second order solitary wave solution of the Euler equations.
This paper solves the integrable CH-γequation for analytical multiple soliton solutions with the Darboux transformation method.Some properties of the soliton solutions are different from the CH equation.
CHEN ChunLi~(1+) LI YiShen~2 ZHANG JinE~3 1 Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China
