Darboux transformation and multi-soliton solutions for some soliton equations

A class of new spectral problems associated with a Broer–Kaup–Kupershmidt and a Boussinesq–Burgers soliton hierarchy are presented. They are used to generate some new soliton equations. The Darboux transformation for these spectral problems is constructed with the help of a gauge transformation. Finally, by applying the Darboux transformation, some new soliton solutions of these soliton equations are obtained. Some interesting solutions of multi-peak soliton have been found.