Abstract
An analysis of the extension of Hamiltonian operators from lower order to higher order of the matrix paves the way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of lower order, new local bi-Hamiltonian coupled KdV systems are proposed. As a consequence of the bi-Hamiltonian structure, they all possess infinitely many symmetries and infinitely many conserved densities.
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