Solitary wave solution to Boussinesq equations

The exact solitary wave solution to the Boussinesq equations, which was given in an,implicit integral form, is further studied in the present note. Through numerical curve fitting, an explicit closed-form empirical solution whose profile is nearly identical to the exact solution is obtained. Discussion and comparison between solitary wave solutions based on the Boussinesq model and higher-order theories of the Euler equation are presented.