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Nonlocal symmetries and exact solutions of a variable coefficient AKNS system. (English) Zbl 1477.76061

Summary: In this paper, nonlocal symmetries of variable coefficient Ablowitz-Kaup-Newell-Segur(AKNS) system are studied for the first time. In order to construct some new 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 reductions and some analytic solutions. For some interesting solutions, such as interaction solutions among solitons and other complicated waves, we give corresponding images to describe their dynamic behavior.

MSC:

76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
76B25 Solitary waves for incompressible inviscid fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q51 Soliton equations
35A30 Geometric theory, characteristics, transformations in context of PDEs

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