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Dromions, dromion lattice, breathers and instantons of the Davey-Stewartson equation. (English) Zbl 1064.35170
Summary: The author studies the abundant localized coherent structures of the Davey-Stewartson (DS) equation. A 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.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
37K40Soliton theory, asymptotic behavior of solutions