The paper is devoted to constructing Auto-Backlund transformations (ABT) and superposi-tion formulas for the solutions of the Drinfeld-Sokolov (DS) systems. The transformationsare derived from pairs of differential substitutions relating different systems of the DS type.The nonlinear superposition formulas for solutions of the DS systems are obtained from theassumption of commutativity of the Bianchi diagram. We indicate a seed solution for eachsystem which can be used to generate multi-soliton solutions. As an application of thesuperposition formulas we construct two-soliton solutions for each of the DS systems.
Balakhnev, M. Y., & Demskoy, D. (2012). Auto-Backlund transformations and superposition formulas for solutions of Drinfeld-Sokolov systems. Applied Mathematics and Computation, 219(8), 3625-3637. https://doi.org/10.1016/j.amc.2012.09.057