In this paper, we establish exact solutions of coupled Higgs equation and Nizhnik-Novikov-Veselov (NNV) system. We apply generalized Kudryashov method (GKM) to seek exact solutions of coupled Higgs equation and NNV system. We find dark soliton solutions of coupled Higgs equation and NNV system via GKM. Then, for proper parameters, we plot 2D and 3D surfaces of some dark soliton solutions that we obtained by using this method. Numerical results together with the graphical demonstrations clearly present the reliability of this method. Also, the proposed method is consonant with the physical structure of such equations.
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