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By using a Lie algebra A1, an isospectral Lax pair is introduced from which a generalized Giachetti-Johnson hierarchy is generated, which reduce to the coupled KdV-MKdV equation, furthermore, the algebro-geometric solutions of the coupled KdV-MKdV equation are constructed in terms of Riemann theta functions.

The generalized Giachetti-Johnson hierarchy and algebro-geometric solutions of the coupled KdV-MKdV equation