Abstract
In this paper, a variable separation approach is used to study the localized coherent structures of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov (GNNV) equation. The abundance of the localized structures of the model is introduced by the entrance of two variables separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the GNNV equation may be dromions, breathers, instantons and ring solitons etc.
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