Auto-Bäcklund transformations and superposition formulas for solutions of Drinfeld–Sokolov systems

摘要

The paper is devoted to constructing Auto-Bäcklund transformations (ABT) and superposition formulas for the solutions of the Drinfeld–Sokolov (DS) systems. The transformations are 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 the assumption of commutativity of the Bianchi diagram. We indicate a seed solution for each system which can be used to generate multi-soliton solutions. As an application of the superposition formulas we construct two-soliton solutions for each of the DS systems.