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

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Abstract
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.