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In this paper, under investigation is the (2+1)-dimensional Nizhnik–Novikov–Veselov equations. The breather wave solutions are derived via the three-wave method. The double-periodic soliton solutions are studied based on a direct function method. Furthermore, the interaction solutions of the lump and periodic waves are investigated by a special function consist of the quadratic polynomial functions and periodic functions. At the same time, we also choose some specific examples to illustrate the dynamic behaviors of nonlinear waves.