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Nonlocal symmetries and exact solutions of variable coefficient AKNS system
Xiangpeng Xin,Linlin Zhang,Yarong Xia,Hanze Liu
Keywords:Nonlocal symmetry, Variable coefficient equations, Exact solution, Lie point symmetry
Abstract:
      In this paper, nonlocal symmetries and exact solutions of variable coefficient Ablowitz-Kaup-Newell-Segur(AKNS) system are studied for the first time. Using lax pair and a nonlocal assumption, nonlocal symmetries of time-dependent coefficient AKNS system are obtained. In order to construct new exact analytic solutions, a new variable is introduced, which can transform nonlocal symmetries into Lie point symmetries. Furthermore, using the Lie point symmetries of closed system, we give out two types of symmetry reduction and some exact analytic solutions. For some interesting solutions, such as interaction solutions among solitons and other complicated waves are discussed in detail, and the corresponding images are given to illustrate their dynamic behavior.