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In this paper, the classifications of classical and nonclassical symmetries to a composite type equation are determined. Firstly, the classification of classical symmetries to the composite equation is determined based on the differential characteristic set algorithm. Secondly, the classification of nonclassical symmetries for the composite equation is determined. First step, adding invariant surface condition and the original equation composed a new system of partial differential equationsdoi:10.12677/pm.2017.74040 fatcat:hzvnb6ntnzfvjkn6jgapr55nxu