The general form of nonlinear evolution equations integrable by matrix gelfand-dikij spectral problem and their group-theoretical and hamiltonian structures

The Gelfand-Dikij spectral problem is considered in the AKNS-technique framework. The general form of nonlinear evolution equations connected with matrix Gelfand-Dikij spectral problem is found. The infinitedimensional abelian group of general Backlund transformations is constructed. The infinite family of Hamiltonian structures connected with the nonlinear equations under consideration is found.