Abstract
A new coupled Burgers equation and a new coupled KdV equation which are associated with [Formula: see text] matrix spectial problem are investigated for complete integrability and covariant property. For integrability, Lax pair and conservation laws of the two new coupled equations with four potentials are established. For covariant property, Darboux transformation (DT) is used to construct explicit solutions of the two new coupled equations.
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