Bäcklund-calogero group and general form of integrable equations for the two-dimensional Gelfand-Dikij-Zakharov-Shabat problem bilocal approach

The general form of the integrable equations and their Bäcklund transformations connected with the general two-dimensional Gelfand-Dikij-Zakharov-Shabat spectral problem is found within the framework of the generalized AKNS method. The bilocal tensor product of the solutions of the spectral problem is used successively, which essentially simplifies the calculations of recursion operators. The transformation properties of the integrable equations and Bäcklund transformations under the gauge group are discussed.