Using the nonlinear constraint and Darboux transformation methods, the (m₁,...,m_N) localized solitons of the hyperbolic su(N) AKNS system are constructed. Here "hyperbolic su(N)" means that the first part of the Lax pair is F_y=JF_x+U(x,y,t)F where J is constant real diagonal and U^*=-U. When different solitons move in different velocities, each component U_ij of the solution U has at most m_im_j peaks as t tends to infinity. This corresponds to the (M,N) solitons for the DSI equation. When all the solitons move in the same velocity, U_ij still has at most m_im_j peaks if the phase differences are large enough.

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