In this paper, we study the abundant localized coherent structures of the Davey–Stewartson (DS) equation which was derived from the fluid dynamics, plasma physics and the self-dual Yang-Mills field. A "universal" formula which is suitable for some other types of (2+1)-dimensional integrable models is used to find some types of dromions and dromion lattice, breathers and instantons of the DS equation. The breathers may breath in their amplitudes, shapes, distances among the peaks and even the number of the peaks.
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Sen‐Yue Lou (2002) studied this question.
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