| Summary: | The nonlocal symmetries for the coupled (2 + 1)-dimensional Burgers system are obtained with the truncated Painlevé expansion method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite symmetry transformations related with the nonlocal symmetries are computed. The multi-solitary wave solution of the (2 + 1)-dimensional coupled Burgers system are presented. By using the consistent tanh expansion method, many interaction solutions among solitons and other types of nonlinear excitations of a (2 + 1)-dimensional coupled Burgers system can be obtained, which include soliton-cnoidal waves, multiple resonant solutions, soliton-error function waves, soliton-rational waves, and soliton-periodic waves.
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