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We aim at presenting Liouville integrable Hamiltonian models with four dependent variables from a specific matrix eigenvalue problem. The Liouville integrability of the resulting models is exhibited through formulating their bi-Hamiltonian formulations. The basic tools are the Lax pair approach and the trace identity. Two illustrative examples consist of novel four-component coupled integrable models of second-order and third-order
YANG et al. (Fri,) studied this question.
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