Darboux transformation of the Drinfeld-Sokolov-Satsuma-Hirota system and exact solutions

A Darboux transformation for the Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations is constructed with the aid of gauge transformations between the Lax pairs. As an application, several types of solutions of the Drinfeld-Sokolov-Satsuma-Hirota system are obtained, including soliton solutions, periodic solutions, rational solutions and others.