Bidirectional soliton solutions of the classical Boussinesq system and AKNS system

In this letter, an alternative method is used to generate the bidirectional soliton solutions of the classical Boussinesq system. We point out that the classical Boussinesq system is gauge equivalent to a member of the AKNS system, give a general formula of the multi-soliton solutions by using Darboux transformation, and present some examples for different cases.