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In this paper, we construct abundant exact solutions of generalized (2+1)-dimensional shallow water wave equation via the Hirota bilinear method and test functions. We obtain exact interaction solutions, such as solitons, lump solutions and lump-periodic solutions for the generalized (2+1)-dimensional shallow water wave equation degenerated by the generalized (3+1)-dimensional shallow water wave equation which introduced by Sakkaravarthi et al.