The Darboux Transformations Of The Boussinesq-like Equations And Its Exact Solutions

The paper studies mainly the N times Darboux transformation of an important soli-ton equation, that is Boussinesq-like equation and its exact solutions.There are three sections in this article. In the first section,the fundamental theory of the Darboux trans-formation are mainly introduced. In the second section,a class of new spectral problems associated with a Broer-Kaup-Kupershmidt and a Boussinesq-Burgers soliton hierarchy are presented,the Darboux transformation for these spectral problems is constructed.By ap-plying the Darboux transformation,we obtain the solutions of multiple soliton interactions. In the third section, connection between the variable-coefficient Boussinesq-like system and a variable-coefficient Broer-Kaup-Kupershmidt (vcBKK)system is revealed under certain constraints.The Darboux transformation for vcBKK system is constructed with the help of a gauge transformation. Finally,by applying the Darboux transformation,soliton solutions of variable-coefficient Boussinesq-like system are obtained.