Abstract
By the use of the extended homogenous balance method, the Bäcklund transformation for a (2+1)-dimensional integrable model, the(2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation, is obtained, and then the NNV equation is transformed into three equations of linear, bilinear, and tri-linear forms, respectively. From the above three equations, a rather general variable separation solution of the model is obtained. Three novel class localized structures of the model are founded by the entrance of two variable-separated arbitrary functions.
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