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The coherent and incoherent interactions between discrete-soliton trains are numerically investigated in lightinduced two-dimensional photonic lattices.The solutions of discrete-soliton trains for diamond and square lattices are obtained by Petviashvili iteration method.It is found that for both the kinds of lattices,two in-phase(outof-phase)discrete-soliton trains attract (repel) each other,and the intermediates are always accompanied with energy transfer.While the interaction forces between two incoherent discrete-soliton trains are always attractive.