Abstract
The general form of nonlinear evolution equations and their Backlund transformations connected with the quadratic in the spectral parameter, Z2-graded, arbitrary-order linear matrix spectral problem is found. The Hamiltonian structure of the integrable equations is discussed. The infinite family of Poisson brackets which corresponds to the class of equations under consideration is given. Relativistic-invariant integrable equations are considered. The explicit forms of elementary and soliton Backlund transformations are found. A nonlinear superposition principle is obtained.
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