On the harmonic superspace language adapted to the Gelfand-Dickey algebra of differential operators

Methods developed for the analysis of nonlinear integrable models are used in the harmonic superspace (HS) framework. These methods, when applied to the HS, can lead to obtain more information about the meaning of integrability in nonlinear physical problems. Among the results obtained, we give the basic ingredients towards building in the HS language the analogue of the Gelfand-Dickey (GD) algebra of pseudo-differential operators. Some useful conventional notations and algebraic structures are also introduced to make the use of the harmonic superspace techniques more accessible.