N-fold Darboux transformation and multi-soliton solutions for the classical Boussinesq–Burgers system

In this paper, we present a new N  -fold Darboux transformation of the classical Boussinesq–Burgers system with the help of a gauge transformation of the spectral problem. As an application, new explicit (2N)(2N)-soliton solutions are obtained. Both the N  -fold Darboux transformation and (2N)(2N)-soliton solutions can be written explicitly in terms of Vandermonde-like determinants.