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In this paper, nonlocal symmetries of variable coefficient Ablowitz-Kaup-Newell-Segur(AKNS) system are discussed for the first time. With lax pair of time-dependent coefficient AKNS system, the nonlocal symmetries are obtained, and they are successfully localized to a Lie point symmetries by introducing a suitable auxiliary dependent variable. Furthermore, using the obtained Lie point symmetries of closed system, we give out two types of symmetry reduction and explicit analytic solutions. For some interesting solutions, the figures are given out to show their dynamic behavior.

NONLOCAL SYMMETRIES AND EXACT SOLUTIONS OF A VARIABLE COEFFICIENT AKNS SYSTEM